Question

A single-degree-freedom spring-mass system is subjected to a sinusoidal force of 10 N amplitude and frequency $\omega$ along the axis of the spring. The stiffness of the spring is 150 N/m, damping factor is 0.2 and the undamped natural frequency is 10$\omega$. At steady state, the amplitude of vibration (in m) is approximately.

• A. 0.05
• B. 0.07
• C. 0.70
• D. 0.90

Answer 1

The correct option is B 0.07

$A=\frac{F_0/s}{\sqrt{{[1-{\left(\frac{\omega }{{\omega }_n}\right)}^2]}^2+{\left(2\xi \frac{\omega }{{\omega }_n}\right)}^2}}$

Given data:

$F=10N$

$s=150N/m$

$\frac{\omega }{{\omega }_n}=\frac{\omega }{10\omega }=0.1$

$\epsilon =0.2$

$\Rightarrow A=\frac{10/150}{\sqrt{[1-(0.1{)}^2{]}^2+[2\times 0.2\times 0.1{]}^2}}=0.07m$