2) Consider the mechanical system depicted below, used to model the needle of an old vinyl record player. This system \"measures\" the grooves of an audio record and outputs them as sound. In this model, the mass is the needle and arm, the force is due to the grooves in the record, and the spring and viscous damper are used to represent other system dynamics. The input is given by $f(t)$, and the output is $y(t)$. Determine the transfer function from $f(t)$ to $y(t)$, that is $G(s) = \frac{y(t)}{f(t)}$, and using MATALB plot the system response to a unit step input. Let $m = 0.2$ kg, $k = 0.1$ N/m, and $b = 0.05$ N-s/m. Assume that the system is initially at rest (zero initial conditions).
