Question

A single degree of freedom spring mass system with viscous damping has spring constant of 10 kN/m. The system is excited by a sinusodial force of amplitude 100 N. If the damping factor (ratio) is 0.25, the amplitude of steady state oscillation at resonance is mm.

Answer 1

Forcing function $=F_{0}sin\omega t$
Given, $F_0=100N$
Damping factor,
$\xi =0.25$
Spring constatn,

k=10 kNm = 10 $\times$ 1000=10000 N.m
$A=\frac{F_0/k}{\sqrt{{\{1-{\left(\frac{\omega }{{\omega }_n}\right)}^2\}}^2+{\left(2\xi \frac{\omega }{{\omega }_n}\right)}^2}}$
At resonance
$\omega ={\omega }_n$
$\therefore A=\frac{\frac{100}{10000}}{2\xi }=\frac{0.01}{2\times 0.25}=0.02$ m
= 20 mm