Consider the second-order control system with closed-loop transfer function as in the picture attached.

For the under-damping control system, it is possible to achieve a response that does not exhibit any oscillation by appropriate choice of the input function r(t) as shown in fig.2 and the desired output will be as shown in fig.3,, FIND THE VALUE OF t1 and A.

the concept is to finding r(t) first, then transfer it to S-domain, after that we need to find Y(s) and transfer it to time-domain, finally, we need to use it with the Y(t) graph to solve it, but I don't know-how, can you help!

r(t) equals 1 for all t greater than t1

02: Consider the second order Contrd syst with closed. 2 525 +2 loop transfer function Ys' (2 for under damping control system, it is possible to achiev anes forse does not exhibit any oscillation by appropriate choice of the input function rH) as shown in Fig. 2 and the desired outfit will be as shown In Fig. 3. Find the value t A&ti. YA) y til for tt ti Fig. 2 Fig. 3 02: Consider the second order Contrd syst with closed. 2 525 +2 loop transfer function Ys' (2 for under damping control system, it is possible to achiev anes forse does not exhibit any oscillation by appropriate choice of the input function rH) as shown in Fig. 2 and the desired outfit will be as shown In Fig. 3. Find the value t A&ti. YA) y til for tt ti Fig. 2 Fig. 3