These are tasks that need to be done in MATLAB. Any help with the coding is greatly appreciated, thanks!

Consider a spring$-$mass system such as one involving the suspension system of a car.

Assuming that the vertical motion at one wheel obeys Hooke's Law and that the

damping force is proportional to the velocity, we can model this system by the

differential equation

$y^{\text{'}\text{'}}+(\frac{c}{a})y^{\text{'}}+(\frac{d}{a})y=(\frac{1}{a})f(t)$

Task $5$ Now suppose the surface of the road contributes an external force described by theforcing

function $f(t)=$esin$(at),$ determine the vertical motion of the spring, $y(t)$

Task $6$ Of course, a free spring would result in a bumpy ride, so we would

want to dampen the spring such that the oscillations decay. Find some reasonable

values for a damping constant c$.$ Illustrate your reasoning by plotting solutions for

different constants $c.$

Task $7$ Find values of $c($other than your $"$c$"$ value$)$ such that the system is

over$-$damped and under$-$damped. Describe the vertical motion of the spring under

these conditions.