RHP zeros in a second-order system have an interesting impact on the system response. Consider the transfer function of an operational amplifier circuit, with a zero equal to 2 in the RHP, as depicted by the following equation:

\[\begin{aligned}G(s) & =\frac{Y(s)}{R(s)} \\& =-\frac{(s-2)}{(s+2)}\end{aligned}\]

For a unit step input \(r(t)\) find:

(a) \(Y(s)\) - the Laplace transform of the system response.

(b) \(Y_{o}(s)\) - the Laplace transform of the system response without the zero.

(c) Show that

\[Y(s)=s Y_{o}(s)-2 Y_{o}(s)\]

(d) Determine the system responses \(y(t)\) and \(y_{o}(t)\).

(e) Plot \(y(t)\) and-2yo \((t)\) and explain what the two graphs illustrate.