$12\mathrm{.}3.$ The location of a load change in a control loop may affect the system response. In the

block diagram shown in Fig. P$12-3,$ a unit$-$step change in load enters at either location $1$

or location $2.$

$($a$)$ What is the frequency of the transient response when the load enters at location $1$ and

when the load enters at location $2?$

$($b$)$ What is the offset when the load enters at location $1$ and when it enters at location $2?$

$($c$)$ Sketch the transient response to a step change in $U_1$ and to a step change in $U_2.$

FIGURE P$12-3$