$[$Q$7$Virtual Experiment$]$

Fun the right values in the code below so you can confirm eq$.8$

Eq $8$: $(\backslash$omega squared$)=\backslash$omega subscript $0$ superscript $2-(\backslash$gamma squared $/4)$

CODE:

import numpy as np

import matplotlib.pyplot as plt

def forced$\_$oscillation$($t$,$ amplitude, frequency, damping$\_$factor, force$\_$amplitude, force$\_$frequency$)$:

natural$\_$frequency $=$ np$.$sqrt$(1-$ damping$\_$factor$**2)$

response $=$ amplitude $*$ np$.$sin$(2*$ np$.$pi $*$ frequency $*$ t $-$ np$.$arctan$($damping$\_$factor $/$ natural$\_$frequency$))$

force $=$ force$\_$amplitude $*$ np$.$sin$(2*$ np$.$pi $*$ force$\_$frequency $*$ t$)$

return response $+$ force

# Parameters

amplitude $=1\mathrm{.}0$

frequency $=1\mathrm{.}0$ # Natural frequency in Hertz

damping$\_$factor $=0\mathrm{.}1$

force$\_$amplitude $=0\mathrm{.}5$

force$\_$frequency $=1\mathrm{.}5$

# Time values

t $=$ np$.$linspace$(0,10,1000)$

# Calculate forced oscillation

oscillation $=$ forced$\_$oscillation$($t$,$ amplitude, frequency, damping$\_$factor, force$\_$amplitude, force$\_$frequency$)$

# Plot the results

plt$.$plot$($t$,$ oscillation, label$=$'Forced Oscillation'$)$

plt$.$plot$($t$,$ force$\_$amplitude $*$ np$.$sin$(2*$ np$.$pi $*$ force$\_$frequency $*$ t$),$ linestyle$=\text{'}--\text{'},$ label$=$'Applied Force'$)$

plt$.$xlabel$(\text{'}$Time$\text{'})$

plt$.$ylabel$(\text{'}$Amplitude$\text{'})$

plt$.$title$(\text{'}$Forced Oscillation Example'$)$

plt$.$legend$()$

plt$.$grid$($True$)$

plt$.$show$()$