This problem considers the frequency response function of a spring$-$mass system described by a sec$-$

ond order linear constant$-$coefficient differential equation. Although we have not yet discussed second

order systems in the course, you should have some familiarity with them from prior ODE classes. As for

the circuit problem, the frequency response function is easily determined once the differential equation

is known.

Derive the differential equation governing the position of the mass $M_0$ relative to its "rest" position.

The position is denoted $y,$ in meters $($m$).$ The input to the system is the force $u$ with unit Newton

$($N$).$ Note that $u$ is indicated in the opposite direction of $y.$

Derive the frequency response function for this system by assuming $u(t)=e^{jt}$ and $y(t)=$

$H{e}^{jt},$ where $H$ is to be determined. Note that $H$ is a function of the forcing frequency $$ but it is

not a function of time. There is no need to simplify $H.$