Question

A damped harmonic oscillator is subjected to a sinusoidal driving frequency whose frequency is altered but amplitude kept constant. It is found that the amplitude of the oscillator increases from 0.02 mm at very low driving frequency to 8.00 mm at a frequency of 100 cps. Obtain the value of (i) quality factor (ii) the relaxation time, (iii) the damping factor.

Answer 1

1)

$Q=\frac f{\Delta f}=400,$

2)

$\tau=\frac{2\pi}{\nu}=\frac{2\pi}{\Delta f}=0.4245~s,$

3)

$k=\frac{\delta}{\sqrt{4\pi^2+\delta^2}}=1.178.$