A springmassdamper system has k 100 Nm m 13 kg and 01 A s

A spring-mass-damper system has k = 100 N/m, m = 13 kg, and = 0.1. A steady-state harmonic force is applied, f(t) = 25 sin(t) N. Determine the forcing frequency, , which produces the maximum response amplitude. What is the maximum response amplitude?

Solution

For maximum conditions...

Forced frequency (w) = natural frequency * (1-2*£² )

=(k /m ) *(1- 2*0.01²)=(100/13) * (1-2*0.01²)

2.75 rad / s.

Maximum amplitude x_max ={F_o÷k} ÷{ 2*£ *(1-£²)}

{25÷100}÷{2*0.1*(1-0.1²)} =1.25 A°