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(Solved): Problem #2: Consider the second-order system defined by: (Y(s))/(U(s))=(2)/(s^(2) 2\zeta \omega _(n) ...
Problem #2: Consider the second-order system defined by:
(Y(s))/(U(s))=(2)/(s^(2) 2\zeta \omega _(n)s 4)If the input
u(t)is a unit step input: 1- For the undamped system where
\zeta =0, sketch the response
y(t). Find the natural frequency
\omega _(n)and the period T of the oscillation and show them clearly on the sketch. (You might use MATLAB for the sketch) 2- For the under-damped system where
\zeta =0.2, show the solution (equation) and sketch the response
y(t). Find the damped natural frequency
\omega _(d), the period
Tof the oscillation, the maximum peak Mp (overshoot), and the settling time ts and show them clearly on the sketch. (Only hand sketch is allowed) 3- For the critically-damped system where
,\zeta =1, sketch the response
y(t). (You might use MATLAB for the sketch)
