$($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 assignment.

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$$ll call this the $$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