Question

In the steady state forced vibration of problem 1 show that (a) the amplitude of the driven system is maximum when p =√ω2 − 2b and

(b) the value of the maximum amplitude is f/2b√ω2 − 2b.

Answer 1

(a) In the steady state forced vibration the amplitude of vibration of the driven system is given by

It is maximum when the denominator (or the square of the denominator) is a minimum. Let

The function u has a minimum or maximum when

Note that the angular frequency p of the periodic impressed force at amplitude resonance is slightly smaller than that at velocity resonance. (b) The maximum amplitude at resonance is