728 lines
58 KiB
Plaintext
728 lines
58 KiB
Plaintext
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{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "bf0cd470",
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"metadata": {},
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"source": [
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"# Exercice"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"id": "c0302414",
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"metadata": {},
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"outputs": [],
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"source": [
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"import pandas as pd\n",
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"import numpy as np\n",
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"from scipy.optimize import curve_fit"
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]
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},
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{
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"cell_type": "markdown",
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"id": "908b1a9d",
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"metadata": {},
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"source": [
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"### Data generation"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"id": "76ccfc6f",
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"metadata": {},
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"outputs": [],
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"source": [
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"# constants\n",
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"g = 10.\n",
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"V0 = 1.\n",
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"H = 1."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"id": "d58ffe3e",
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"metadata": {},
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"outputs": [],
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"source": [
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"# Model \n",
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"l = V0 * np.sqrt(2.*H/g)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "9a03ead6",
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"metadata": {},
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"source": [
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"### Données\n",
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"pour file \"V1msHvariable.csv\""
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"id": "dd458e01",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"0.40 0.80 0.01\n",
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"0.42 0.90 0.01\n",
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"0.45 1.00 0.01\n",
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"0.47 1.10 0.01\n",
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"0.49 1.20 0.01\n"
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]
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}
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],
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"source": [
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"#\n",
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"error = 0.01\n",
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"for h in [0.8, 0.9,1,1.1,1.2]:\n",
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" l = V0 * np.sqrt(2.*h/g)\n",
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" print('{0:.2f} {1:0.2f} {2:.2f}'.format(l,h,error))"
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]
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},
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{
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"cell_type": "markdown",
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"id": "a06afab7",
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"metadata": {},
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"source": [
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"### Données\n",
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"pour file \"H1mVvariable.csv\""
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"id": "ca4407db",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"0.45 1.00 0.10\n",
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"0.54 1.20 0.10\n",
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"0.67 1.50 0.10\n",
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"0.89 2.00 0.10\n",
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"1.34 3.00 0.10\n"
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]
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}
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],
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"source": [
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"error = 0.1\n",
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"for v in [1, 1.2,1.5,2,3]:\n",
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" l = v * np.sqrt(2.*H/g)\n",
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" print('{0:.2f} {1:0.2f} {2:.2f}'.format(l,v,error))"
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]
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},
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{
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"cell_type": "markdown",
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"id": "81b6f7b3",
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"metadata": {},
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"source": [
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"## Solution"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"id": "a748d198",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/html": [
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"<img src=\"experience.png\" width=\"500\" height=\"500\"/>"
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],
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"text/plain": [
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"<IPython.core.display.Image object>"
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]
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},
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"execution_count": 6,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"# import image module\n",
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"from IPython.display import Image\n",
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" \n",
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"# get the image\n",
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"Image(url=\"experience.png\", width=500, height=500)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "301b6ab8",
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"metadata": {},
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"source": [
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" Une bille supposée ponctuelle avec une vitesse horizontale $V_0$ tombe d'une table de hauteur $H$ et rencontre le sol à une longueur $L$.\n",
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"\n",
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"Nous disposons de deux fichiers de mesures expérimentales (fichiers formatés csv séparés par des \";\")\n",
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"- \"V1msHvariable.csv\" expérience de mesure de la longueur $L$ à vitesse $V_0=1 \\ m/s$ constante pour des différentes hauteurs $H$ avec l'erreur correspondante\n",
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"- \"H1mVvariable.csv\" expérience de mesure de la longueur $L$ à hauteur $H= 1 \\ m$ constante pour des différentes vitesses $V_0$ avec l'erreur correspondante\n",
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"\n",
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"On propose un modèle pour la longueur $L$\n",
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"\n",
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"$$ L = C V_0^\\alpha H^\\beta $$\n",
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"\n",
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"nous allons évaluer les coefficients $\\alpha$ et $\\beta$, ainsi que la constante $C$."
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]
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},
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{
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"cell_type": "markdown",
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"id": "bb58b946",
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"metadata": {},
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"source": [
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"### Point 1.1\n",
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"En utilisant la bibliothèque Pandas, lisez le fichier \"V1msHvariable.csv\" et définisez les variables $L$, $H$, \n",
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"et $erreur$ (de la mesure de hauteur)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"id": "8aa94441",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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" L H error\n",
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"0 0.40 0.8 0.01\n",
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"1 0.42 0.9 0.01\n",
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"2 0.45 1.0 0.01\n",
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"3 0.47 1.1 0.01\n",
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"4 0.49 1.2 0.01\n"
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]
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}
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],
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"source": [
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"d = pd.read_csv(\"V1msHvariable.csv\",delimiter=\";\")\n",
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"print(d)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"id": "296b12e0",
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"metadata": {},
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"outputs": [],
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"source": [
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"d.head()\n",
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"# taking values from headers\n",
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"L = d[\"L\"]\n",
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"H = d[\"H\"]\n",
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"e = d[\"error\"]"
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]
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},
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{
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"cell_type": "markdown",
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"id": "fc7a10ed",
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"metadata": {},
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"source": [
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"### Point 1.2\n",
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"Faites une figure de $L$ vs $H$ avec barres d'erreur"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"id": "d8aab11d",
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"metadata": {},
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"outputs": [],
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"source": [
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"import matplotlib.pyplot as plt"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"id": "67ec753b",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"<matplotlib.legend.Legend at 0x7f84498dfc70>"
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]
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},
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"execution_count": 10,
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"metadata": {},
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"output_type": "execute_result"
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},
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{
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"data": {
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"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 432x432 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {
|
||
|
|
"needs_background": "light"
|
||
|
|
},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"fig = plt.figure(figsize=(6,6)) # s\n",
|
||
|
|
"ax = plt.subplot() \n",
|
||
|
|
"ax.errorbar(H,L,e, marker='.', linestyle=\"none\", label=\"data\")\n",
|
||
|
|
"ax.set_title(\"L vs H\")\n",
|
||
|
|
"ax.set_xlabel(\"H[m]\")\n",
|
||
|
|
"ax.set_ylabel(\"L[m]\")\n",
|
||
|
|
"ax.legend()"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"id": "a84939cd",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"### Point 1.3\n",
|
||
|
|
"Utilisez la fonction \"curve_fit\" pour faire une regression linéaire des données exprimées en une échelle log-log\n",
|
||
|
|
"et trouve la valeur de $\\alpha$"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 11,
|
||
|
|
"id": "4d6afbe8",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"# fit\n",
|
||
|
|
"def func(x, a, b):\n",
|
||
|
|
" return a * x + b"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 12,
|
||
|
|
"id": "db8be79d",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"from scipy.optimize import curve_fit"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 13,
|
||
|
|
"id": "b1b62edc",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"popt= curve_fit(func, np.log(H), np.log(L))"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 14,
|
||
|
|
"id": "10616c91",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"name": "stdout",
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"a = 0.512\n",
|
||
|
|
"b= -0.805\n"
|
||
|
|
]
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"popt[0]\n",
|
||
|
|
"a=popt[0][0]\n",
|
||
|
|
"b=popt[0][1]\n",
|
||
|
|
"print(\"a = %.3f\" % a)\n",
|
||
|
|
"print(\"b= %.3f\" % b)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"id": "763aab30",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"### Point 1.4\n",
|
||
|
|
"Faites un figure log-log de $L$ vs $H$ en ajoutant la regression linéaire trouvée dans le point précédent"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 15,
|
||
|
|
"id": "5403d854",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"text/plain": [
|
||
|
|
"[]"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 15,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 432x432 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {
|
||
|
|
"needs_background": "light"
|
||
|
|
},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"fig = plt.figure(figsize=(6,6)) # s\n",
|
||
|
|
"ax = plt.subplot() \n",
|
||
|
|
"ax.errorbar(H,L,e, marker='.', linestyle=\"none\", label=\"data\")\n",
|
||
|
|
"ax.plot(H,np.exp(b)*H**a,\"-\",label=\"model\")\n",
|
||
|
|
"ax.set_title(\"with error bars\")\n",
|
||
|
|
"ax.set_title(\"L vs H\")\n",
|
||
|
|
"ax.set_xlabel(\"H[m]\")\n",
|
||
|
|
"ax.set_ylabel(\"L[m]\")\n",
|
||
|
|
"ax.legend()\n",
|
||
|
|
"ax.loglog()"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"id": "07f7c827",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"Estimation de la constante $C$"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 16,
|
||
|
|
"id": "d619b153",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"name": "stdout",
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"0 0.447214\n",
|
||
|
|
"1 0.442719\n",
|
||
|
|
"2 0.450000\n",
|
||
|
|
"3 0.448127\n",
|
||
|
|
"4 0.447307\n",
|
||
|
|
"dtype: float64\n"
|
||
|
|
]
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"C=L/H**0.5\n",
|
||
|
|
"print(C)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"id": "9f02fc0f",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"## Partie 2\n",
|
||
|
|
"Etude de la longueur $L$ à hauteur $H= 1 \\ m$ constante pour des différentes vitesses $V_0$ "
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"id": "4692da2f",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"### Point 2.1\n",
|
||
|
|
"En utilisant la bibliothèque Pandas, lisez le fichier \"H1mVvariable.csv\" et définisez les variables $L$, $V_0$, \n",
|
||
|
|
"et $erreur$ (de la mesure de vitesse)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 17,
|
||
|
|
"id": "86a78bb1",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"name": "stdout",
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
" L V error\n",
|
||
|
|
"0 0.45 1.0 0.1\n",
|
||
|
|
"1 0.54 1.2 0.1\n",
|
||
|
|
"2 0.67 1.5 0.1\n",
|
||
|
|
"3 0.89 2.0 0.1\n",
|
||
|
|
"4 1.34 3.0 0.1\n"
|
||
|
|
]
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"d = pd.read_csv(\"H1mVvariable.csv\",delimiter=\";\")\n",
|
||
|
|
"print(d)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 18,
|
||
|
|
"id": "9d9b92cc",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"# taking values from headers\n",
|
||
|
|
"L = d[\"L\"]\n",
|
||
|
|
"V = d[\"V\"]\n",
|
||
|
|
"e = d[\"error\"]"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"id": "bcc73921",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"### Point 2.2\n",
|
||
|
|
"Faites une figure de $L$ vs $V_0$ avec barres d'erreur"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 19,
|
||
|
|
"id": "2b001194",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"text/plain": [
|
||
|
|
"<matplotlib.legend.Legend at 0x7f8428d243a0>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 19,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 432x432 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {
|
||
|
|
"needs_background": "light"
|
||
|
|
},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"fig = plt.figure(figsize=(6,6)) # s\n",
|
||
|
|
"ax = plt.subplot() \n",
|
||
|
|
"ax.errorbar(V,L,e, marker='.', linestyle=\"none\", label=\"data\")\n",
|
||
|
|
"ax.set_title(\"with error bars\")\n",
|
||
|
|
"ax.set_title(\"L vs $V_0$\")\n",
|
||
|
|
"ax.set_xlabel(\"$V_0$[m/s]\")\n",
|
||
|
|
"ax.set_ylabel(\"L[m]\")\n",
|
||
|
|
"ax.legend()"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"id": "70f7b0cd",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"### Point 2.3\n",
|
||
|
|
"Utilisez la fonction \"curve_fit\" pour faire une regression linéaire des données exprimées en une échelle log-log\n",
|
||
|
|
"et trouve la valeur de $\\beta$"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 20,
|
||
|
|
"id": "21162560",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"popt= curve_fit(func, np.log(V), np.log(L))"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 21,
|
||
|
|
"id": "ad96315b",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"name": "stdout",
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"a = 0.991\n",
|
||
|
|
"b = -0.800\n"
|
||
|
|
]
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"popt[0]\n",
|
||
|
|
"a=popt[0][0]\n",
|
||
|
|
"b=popt[0][1]\n",
|
||
|
|
"print(\"a = %.3f\" % a)\n",
|
||
|
|
"print(\"b = %.3f\" % b)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"id": "8b31f498",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"### Point 2.4\n",
|
||
|
|
"Faites un figure log-log de $L$ vs $V_0$ en ajoutant la regression linéaire trouvée dans le point précédent"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 22,
|
||
|
|
"id": "78a36fc1",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"text/plain": [
|
||
|
|
"[]"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 22,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAZ8AAAGMCAYAAAAFoK+hAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/MnkTPAAAACXBIWXMAAAsTAAALEwEAmpwYAAAgs0lEQVR4nO3deZScdZ3v8fc3SUNAQ4hBrkogCYTLGiQkQFSiM4BcFhNERha5MxqQRM94j7NcvegswRFkRrgzgDiyyKJjWDSCA47LCIoIJIoZkMWAhpjElotAB2MIiST09/7RBTSV7qSXquep5f06p8/pevpXT30rRfPp51NPVUVmIklSkUaUPYAkqf0YPpKkwhk+kqTCGT6SpMIZPpKkwhk+kqTCGT6SpMIZPlIBImJlRBxdwO2MjIgNEXFgHz+7ISKurfcM0kCMKnsASbWTmS9GxKPAAcDDL22PiBnAu4B9yppN6s0jH6lBRMQ5EbGoatslEXFp5fv/ExG/iYh1EfFYRBzVz64eBvav2nYhcFFmPlH7yaXB88hHahw3AH8fETtl5u8jYiRwCnBSROwDfAQ4NDOfiIhJwMh+9vMIMOOlCxExG9gbOKGu00uD4JGP1CAycxXwX8C7K5uOBJ7PzCXAi8D2wP4R0ZGZKzPz8X529fKRTyXA/hH4m8x8vrLt/Ij4UUQsiogd63ePpP4ZPlJjuR44vfL9+yqXyczlwF8A5wJPRcSNEfGmfvbxCLB3RHQAZwEbgS8DVE5E2CszZwG3A2fW525IW2f4SI3la8AfRcQE4CQq4QOQmddn5hHARCCBf+pnHyvpCZxp9ITVX+Urb18/C/h25ftvA0fUeH5pQAwfqTgdETG619cWz7lm5tPAncC1wK8ycxlAROwTEUdGxPb0BMsGeqq4LVSCZhlwOfDjzPxhrx+PA9ZWvl8LvK42d00aHMNHKs636AmNl77O7Wfd9cDR9Drqoef5nn8EngGeBHYFPrmV23oYOBD4eNX2Z4Gxle/HAmsGPL1UQ+GHyUntIyKmAp/IzPdFxDxg+8z8XNlzqf14qrXURjLzoYhYFRE/Ap4C/qzsmdSePPKRJBXO53wkSYUzfCRJhTN8JEmFM3wkSYXzbLd+7LLLLjlp0qSyx5CkprJ06dJnMvP121pn+PRj0qRJ/PSnPy17DElqKhGxaiDrrN0kSYUzfCRJhTN8JEmF8zmfQdi0aROdnZ1s3Lix7FFKNXr0aCZMmEBHR0fZo0hqUobPIHR2djJmzBgmTZpERJQ9Tikyk66uLjo7O5k8eXLZ40hqUtZug7Bx40bGjx/ftsEDEBGMHz++7Y/+JA2P4TNI7Rw8L/HfQNJwGT5tbNKkSTzzzDPDXiNJg2X4SJIKZ/g0mZUrV7LvvvvywQ9+kAMPPJAzzjiD22+/nbe97W3svffe/OQnP2HNmjW8+93v5qCDDmLmzJk8+OCDAHR1dXHMMccwbdo05s+fT+/PcvrKV77CYYcdxsEHH8z8+fN58cUXy7qLktqA4dOEli9fzkc/+lEefPBBHn30Ua6//nruvvtuLrroIj7zmc+wYMECpk2bxoMPPshnPvMZ/uzPej6s8lOf+hRHHHEE999/P3PmzGH16tUALFu2jJtuuol77rmHBx54gJEjR7Jw4cIy76KkFuep1kP17XPgyYdqu883TIXj/nGbyyZPnszUqVMBOOCAAzjqqKOICKZOncrKlStZtWoVX//61wE48sgj6erqYu3atdx1113cfPPNAJxwwgmMGzcOgDvuuIOlS5dy6KGHArBhwwZ23XXX2t43SerF8GlC22+//cvfjxgx4uXLI0aMYPPmzYwateXD+tIZan2dqZaZvP/97+eCCy6o08SS9GqGz1AN4AilLG9/+9tZuHAhf/d3f8edd97JLrvswk477fTy9r/927/l29/+Ns8++ywARx11FCeeeCJ/+Zd/ya677sqaNWtYt24dEydOLPmeSCrSqVcsBuCm+W+p+20ZPi3o3HPPZe7cuRx00EHsuOOOfOlLXwJgwYIFnH766RxyyCG84x3vYI899gBg//3357zzzuOYY46hu7ubjo4OPv/5zxs+kuomep/xpFfMmDEjqz/PZ9myZey3334lTdRY/LeQWk8tjnwiYmlmztjWOs92kyQVzvCRJBXO8JEkFc7wkSQVzvCRJBXO8JEkFc7wqbNTr1j88umLtXbuuedy0UUX9fvzb3zjG/z85z+vy21L0nAYPi3M8JHUqAyfJnP++eezzz77cPTRR/PYY48BcNVVV3HooYfy5je/mZNPPpnnn3+ee++9l1tvvZWPfexjHHzwwTz++ON9rpOkMhg+dbZu4yZ+87sNLF317LD3tXTpUm688Ubuv/9+br75Zu677z4A3vOe93Dffffxs5/9jP3224+rr76at771rcyZM4cLL7yQBx54gL322qvPdZJUBsOnjpauepZHn1xH57MbOOOLS4YdQD/60Y846aST2HHHHdlpp52YM2cOAA8//DCzZs1i6tSpLFy4kEceeaTP6w90naT2VMs/lrfF8KmjJSu66K68dd6mzd0sWdE17H329ZEIH/jAB7jssst46KGHWLBgARs3buzzugNdJ6n9vPLH8vM1+WN5WwyfOpq553hGVLKiY9QIZu45flj7e/vb384tt9zChg0bWLduHbfddhsA69at441vfCObNm161SeQjhkzhnXr1r18ub91krTk0dWQ3UDU7I/lrTF86mj6xHHs+4YxTBi3Aws/OJPpE8cNa3+HHHIIp556KgcffDAnn3wys2bNAuDTn/40hx9+OO985zvZd999X15/2mmnceGFFzJt2jQef/zxftdJanOr7mXm/R9nOzYRZE3+WN4WP1KhH7X6SIUiP5ypSH6kgtQCurvhnn+B758H4yZz5qaP8YvN/41LTps25D+W/UgFSVL/1j8DC/8E7vgHOOAkmP9D1r92ErvtvMOwW5qB8JNM66zVjngktYBV98KiM+H5NfCui2H6B6CPk5nqyfCRpHZRVbPxwa/CGw8qZRTDZ5Ays8/TnduJzxNKTWj9M3DzPHj8DjjwZJh9CWw/prRxDJ9BGD16NF1dXYwfP75tAygz6erqYvTo0WWPImmgGqBmq2b4DMKECRPo7Ozk6aefLnuUUo0ePZoJEyaUPYakbWmgmq2a4TMIHR0dTJ48uewxJGnbGqxmq2b4SFKracCarZrhI0mt4uWa7XwYN6mharZqho8ktYLqmu1dF8Poncqeql+GjyQ1uyao2aoZPpLUrJqoZqtm+EhSM2qymq2a4SNJzaZONVuR70Vp+EhSs2jimq2a4SNJzWD9M3DLfFh+Oxzwnp4XjTZRzVbN8JGkRveqmu1fYPrchj+bbVsMH0lqVC1Us1UzfCSpEbVYzVbN8JGkRtOCNVs1w0eSGkUL12zVDB9JagQtXrNVM3wkqWyr7oVFZ8HzXS1bs1UzfCSpLFvUbLe3bM1WzfCRpDK0Wc1WzfCRpKK1Yc1WzfCRpKK0cc1WzfCRpCK0ec1WzfCRpHqzZtuC4SNJ9WLN1i/DR5LqwZptqwwfSaq1VYsr781mzdYfw0eSaqW7G+65GL5/HoybaM22FYaPJNWCNdugGD6SNFzWbINm+EjSUFmzDZnhI0lDYc02LIaPJA2WNduwGT6SNFDWbDVj+EjSQFiz1ZThI0nbYs1Wc4aPJPXHmq1uDB9J6os1W10ZPpJUrXfNdsI/w4wzrdlqzPCRpJdYsxXG8JEksGYrmOEjSdZshTN8JLUva7bSGD6S2tP6LrhlnjVbSQwfSe3Hmq10ho+k9rFFzfY9eOOby56qLRk+ktqDNVtDMXwktT5rtoZj+EhqXdZsDastwiciXgP8K/ACcGdmLix5JEn1Zs3W0EaUPcBQRcQ1EfFURDxctf3YiHgsIpZHxDmVze8BFmXm2cCcwoeVVKxVi+HyI+BXP+qp2f7kGoOnwTRt+ADXAcf23hARI4HPA8cB+wOnR8T+wATg15VlLxY4o6QidXfDj/4ZrjsBOkb31GyHnuXzOw2oaWu3zLwrIiZVbT4MWJ6ZKwAi4kbgRKCTngB6gOY
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 432x432 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {
|
||
|
|
"needs_background": "light"
|
||
|
|
},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"fig = plt.figure(figsize=(6,6)) # s\n",
|
||
|
|
"ax = plt.subplot() \n",
|
||
|
|
"ax.errorbar(V,L,e, marker='.', linestyle=\"none\", label=\"data\")\n",
|
||
|
|
"ax.plot(V,np.exp(b)*V**a,\"-\",label=\"model\")\n",
|
||
|
|
"ax.set_title(\"with error bars\")\n",
|
||
|
|
"ax.set_title(\"L vs $V_0$\")\n",
|
||
|
|
"ax.set_xlabel(\"$V_0$[m/s]\")\n",
|
||
|
|
"ax.set_ylabel(\"L[m]\")\n",
|
||
|
|
"ax.legend()\n",
|
||
|
|
"ax.loglog()"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"id": "b27babbe",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"Estimation de la constante $C$"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 23,
|
||
|
|
"id": "6ae3c7c3",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"name": "stdout",
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"0 0.450000\n",
|
||
|
|
"1 0.450000\n",
|
||
|
|
"2 0.446667\n",
|
||
|
|
"3 0.445000\n",
|
||
|
|
"4 0.446667\n",
|
||
|
|
"dtype: float64\n"
|
||
|
|
]
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"C1=L/V\n",
|
||
|
|
"print(C1)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 24,
|
||
|
|
"id": "e34d2bdb",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"name": "stdout",
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"0.447073328032969 0.44766666666666677\n"
|
||
|
|
]
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"print(C.mean(),C1.mean())"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"id": "c215342d",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"Le modèle peut s'écrire donc\n",
|
||
|
|
"$$L = C V H^{1/2}$$\n",
|
||
|
|
"avec $C=0.447$.\n",
|
||
|
|
" L'unité de $C$ est $\\sqrt{T^2/L}$\n",
|
||
|
|
"$$ L = [C] L/T L^{1/2}$$.\n",
|
||
|
|
"\n",
|
||
|
|
"Comme le moteur de la chute c'est la gravité et $[g] = L/T^2$ nous pouvons écrire\n",
|
||
|
|
"$$ C = \\sqrt{2/ g}$$ alors\n",
|
||
|
|
"$$ L = V_0 \\sqrt{ \\frac{2 H}{g}}$$."
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": null,
|
||
|
|
"id": "ca1f0efd",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": []
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"metadata": {
|
||
|
|
"kernelspec": {
|
||
|
|
"display_name": "Python 3 (ipykernel)",
|
||
|
|
"language": "python",
|
||
|
|
"name": "python3"
|
||
|
|
},
|
||
|
|
"language_info": {
|
||
|
|
"codemirror_mode": {
|
||
|
|
"name": "ipython",
|
||
|
|
"version": 3
|
||
|
|
},
|
||
|
|
"file_extension": ".py",
|
||
|
|
"mimetype": "text/x-python",
|
||
|
|
"name": "python",
|
||
|
|
"nbconvert_exporter": "python",
|
||
|
|
"pygments_lexer": "ipython3",
|
||
|
|
"version": "3.9.7"
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"nbformat": 4,
|
||
|
|
"nbformat_minor": 5
|
||
|
|
}
|