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ME3255S2017/lecture_21/lecture_21.ipynb

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"![q1](q1.png)\n",
"\n",
"![q2](q2.png)\n",
"\n",
"## Reduce Noise in derivative of data\n",
"\n",
"![reduce noise](reduce_noise.png)\n",
"\n",
"- Turn the volume down!\n",
"\n",
"- Use robust statistics like median and mean absolute deviation\n",
"\n",
"- Gauss quadrature\n",
"\n",
"- Put a filter on it\n",
"\n",
"- Take the average\n",
"\n",
"- Low-pass filter\n",
"\n",
"- Expand the Taylor series\n",
"\n",
"- Fit a function and derive that\n",
"\n",
"\n"
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"error: subscript indices must be either positive integers less than 2^31 or logicals\n",
"ans =\n",
"\n",
" 1 100\n",
"\n"
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],
"source": [
"x=linspace(-pi,pi);\n",
"y_smooth=sin(x);\n",
"y_noise =y_smooth+rand(size(x))*0.1-0.05;\n",
"\n",
"% Smooth data\n",
"N=20; % average data between 10 points (forward/backward)\n",
"y_data=[y_noise(N/2:-1:1) y_noise y_noise(end:-1:end-N/2+1)];\n",
"y_filter=y_data;\n",
"for i=6:length(x)\n",
" y_filter(i)=mean(y_data(i-10:i));\n",
"end\n",
"y_filter=y_filter(N/2:end-N/2-1);\n",
"size(y_filter)\n",
"plot(x,y_filter,x,y_noise,'.')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Homework Review\n",
"\n",
"### HW #4\n",
"\n",
"![collar mass](../HW4/collar_mass.png)\n",
"\n",
"$E_{total}=m x_C g\\sin(\\theta)+\\frac{K}{2}\\left(0.5 - \\sqrt{0.5^2+(0.5-x_C)^2}\\right)^{2}$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"```matlab\n",
"% Define function ...\n",
"function collar_potential_energy(x,theta)\n",
" % function to evaluate E_total\n",
" Etotal = m*x*g.*sin(theta)+K/2*(0.5-sqrt(0.5^2+(0.5-x).^2);\n",
"end\n",
"\n",
"% solve for x\n",
"\n",
"x=goldmin(@(x) collar_potential_energy(x,theta),xl,xu)\n",
"```"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## HW #5\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Initial Value Problem"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Octave",
"language": "octave",
"name": "octave"
},
"language_info": {
"file_extension": ".m",
"help_links": [
{
"text": "MetaKernel Magics",
"url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
}
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