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Peal Maximum Value of a Feedback Control System

In this attached question P(s) refers to the plant transfer function and Y(S) is the output of the system.
I have also attached a schematic of how the system i think looks like. Please provide solutions to all except part c.

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Band-Pass System

Ty/d = k (2ps/Wn)/[ (s/Wn)^2 + 2ps/Wn +1 ]
p = damping factor
Wn = Natural Frequency in rad/sec

Unit step response:

y(t) = Be^(-a*t)*Sin(Wd*t), where
B = k2p/sqrt(1-p^2),
a = p*Wn, and
Wd = Wn*sqrt(1-p^2)

(a)

Now, to find the peak(maximum ...

Solution Summary

The solution utilises various equations from the relevant theory involving the dampening factor unit step response to find the peak maximum value of the given band-pass system in a clear, easy to follow manner.

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