{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
" MAC0209 - Modelagem e Simulação \n",
"\n",
"Roberto M. Cesar Jr. (IME-USP)\n",
"\n",
"Roberto Hirata Jr. (IME-USP)\n",
"***\n",
" Análise dos dados de queda livre: experimento realizado em aula \n",
"***"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Preâmbulo"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import pandas as pd\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Acelerômetro"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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/pt2pqlXAd6qa/RR1ecSajVuoHD6qjrUWiyWrN8Z8AV+dsrCei+aql6fR4+q3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\n8A3DMEqE/wftlmMf0h+0hgAAAABJRU5ErkJggg==\n",
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