Control Systems...

The output of a standard second order system for a unit – step input is given as

\(y\left( t \right) = 1 - \frac{2}{{\sqrt 3 }}{e^{ - t}}\cos \left( {\sqrt 3 t - \frac{\pi }{3}} \right)\)

The roots of a second order system are located at -1 + j2 and -1 – j2. What is the value of maximum % overshoot if the system is excited by unit step input?

A system has a damping ratio of 1.25, a natural frequency of 200 rad/s and DC gain of 1.

A system with transfer function  \(\frac{1}{{\tau s + 1}}\) subjected to a step input takes 15 seconds to reach 60% of the step height. The value of τ (Correct up to two decimal places) is ___ (in sec)