160 lines
35 KiB
Plaintext
160 lines
35 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 72,
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"id": "5bef2913-4855-471d-9594-5ec45c029048",
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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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"Length: 143.2 mm\n",
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"Freq: 2.822 Hz\n"
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]
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}
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],
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"source": [
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"import math\n",
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"import numpy as np\n",
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"from pint import UnitRegistry\n",
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"unit = UnitRegistry()\n",
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"unit.formatter.default_format = \"~\"\n",
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"\n",
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"\n",
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"# Parameters\n",
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"spring_constant = 1.1 * 4 * unit.N / unit.mm\n",
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"spring_length_resting = 112 * unit.mm\n",
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"\n",
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"weight_total = 14 * unit.kg\n",
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"\n",
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"dampening = 1 * unit.N / (unit.m / unit.s)\n",
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"\n",
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"def spring_length_at(weight):\n",
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" return (weight * unit.standard_gravity / spring_constant + spring_length_resting).to(unit.mm)\n",
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"\n",
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"def resonant_freq_at(weight):\n",
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" return (1 / (2 * math.pi) * np.sqrt(spring_constant / weight)).to(unit.Hz)\n",
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"\n",
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"spring_length = spring_length_at(weight_total)\n",
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"f0 = resonant_freq_at(weight_total)\n",
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"\n",
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"print(f\"Length: {spring_length:~.1f}\")\n",
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"print(f\"Freq: {f0:~.3f}\")"
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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": 73,
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"id": "f21d84d9-c7a1-4fd2-aa32-136f04db32e5",
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"metadata": {
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"editable": true,
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"slideshow": {
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"slide_type": ""
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},
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"tags": []
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},
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"outputs": [
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{
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"data": {
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"text/html": [
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"0.00201455741006345"
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],
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"text/latex": [
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"$0.00201455741006345$"
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],
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"text/plain": [
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"<Quantity(0.00201455741, 'dimensionless')>"
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]
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},
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"execution_count": 73,
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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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"def lehr_dampening_factor(d, k, m):\n",
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" return d / (2 * np.sqrt(m * k))\n",
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"\n",
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"lehr_dampening = lehr_dampening_factor(dampening, spring_constant, weight_total)\n",
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"lehr_dampening.ito_reduced_units()\n",
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"lehr_dampening"
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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": 74,
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"id": "b71de7db-a7fb-4d3a-9dd2-de8e107700a6",
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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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"Text(0.5, 0, 'Excitation Frequency')"
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]
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},
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"execution_count": 74,
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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 640x480 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"def amplitude_ratio(lehr, f0, f):\n",
|
|
" eta = f / f0\n",
|
|
" return 1 / np.sqrt((1 - eta**2)**2 + (2 * eta * lehr)**2)\n",
|
|
"\n",
|
|
"f_in = np.logspace(0, 3.5, 100) * unit.Hz\n",
|
|
"ratio = amplitude_ratio(lehr_dampening, f0, f_in)\n",
|
|
"\n",
|
|
"import matplotlib.pyplot as plt\n",
|
|
"plt.plot(f_in, ratio)\n",
|
|
"plt.xscale('log')\n",
|
|
"plt.ylim(0.000001, 10)\n",
|
|
"plt.yscale('log')\n",
|
|
"plt.ylabel(\"Dampening Ratio\")\n",
|
|
"plt.xlabel(\"Excitation Frequency\")"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "fea96fd4-46e1-4f07-8fb4-25ccc0ee82a5",
|
|
"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": "3.13.3"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 5
|
|
}
|