Response of a damped system under a Harmonic force | Complete Lecture

Vibration of a damped mechanical system under harmonic excitation force has explained in this lecture. Damped vibrating system the characteristic is given by a second order non homogeneous differential equation. The total solution of the differential equation is then the sum of the exponential functions found from the complementary function (which are just the same as for free damped vibration) and the phase shift cosine function of the particular integral solution.The effects of the exponential terms will be damped out shortly after the start of the vibration only particular integral part remain as a steady state vibration.