Question

A mass-spring damper system with force as input and displacement of the mass as output has a transfer function
$G\left(s\right)=\frac{1}{(s^2+24s+900)}$
A force input F(t)= 10 sin(70t) Newtons is applied at time t = 0 sec. A beam from an optical stroboscope is focused on the mass. In steady state, the strobe frequency in hertz at which the mass appears to be stationary is

• A. $\frac{5}{\pi }$
• B. $\frac{50}{\pi }$
• C. $\frac{15}{\pi }$
• D. $\frac{35}{\pi }$

Answer 1

The correct option is D $\frac{35}{\pi }$

At steady state, only magnitude and phase of input change, frequency does not change.

$\omega =70$

$f=\frac{70}{2\pi }=\frac{35}{\pi }$