Problem $4(25$ pts$)$:

For this problem, consider the block diagram below:

Your tasks:

A$.$ Derive the transfer function $H(s)=x\frac{s}{F}(s)$ for the given block diagram. $(10$ pts$)$

B$.$ Does the system have a natural frequency and damping ratio? If so$,$ what are they? $(7$ pts $)$

C$.$ Determine the response of the system $x(t)$ if the input $f(t)$ is the unit delta function, $(t).(8$ pts$)$