$($b$)$ Let's consider the following two driving amplitudes:

$($i$)f_0=0\mathrm{.}4$

$($ii$)f_0=0\mathrm{.}7.$

Create an $m-$file to produce plots of solution curves to the two driving amplitudes.

Your code should call osc.m $($found in part a$)),$ and ode$45.$

Set initial conditions to be $y(0)=y^{}(0)=0.$

The domain of $t$ should be $0,1000.$

Name the m$-$file you used plotsoln.m$,$ and submit it as part of your assign$-$

ment.

In both cases, your solution should be oscillatory and should "settle down into its

final rhythm$"$ after about $t$~~$600$ or so$.$

What is the approximate amplitude of the solution's final waveform for the two

driving amplitudes $($we$\text{'}$ll call this the "final amplitude"$)?$

For each value of $f_0,$ submit plots of the solution curves.

$($c$)$ We now investigate the relationship between $f_0$ and the waveform's final amplitude.

Write another program called drive.m$.$ This code should find the waveform's final

amplitude for $20$ different values of $f_0$ between $0\mathrm{.}4$ and $0\mathrm{.}7.$

Submit a plot which summarises this data. How does the final amplitude respond

to changes in $f_0?$

Submit the plot, and drive.m as part of your assignment.