what is undamped oscillation Why does the real part of the t

what is undamped oscillation? Why does the real part of the transfer function have to be zero in this case??

Solution

The oscillations which doesn\'t die out and maintains constant amplitude as time tends to infinity.

If there exit pure imaginary roots then the system exhibits sustained or undamped oscillations.

In general the roots of the characteristic equatio represents the damping nature which indicates that the oscillations will die out as time tends to infinity.Hence to exhibit sustained or undamped oscillations the real part should be zero i.e., the roots should lie on imaginary axis