Question

Consider a resonator with ω0 = 100 rad/sec and a Q factor of 100. Calculate the time takes it to settle within 2% of the final value when excited with a unit force.

Answer 1

Answer:

8 s

Explanation:

Damping factor, F is given by

$F=\frac {1}{2Q}$ where Q is quality factor

Also, we know that the settling time, T is given by

$T=\frac {4}{FW}$ where W is the resonant frequency.and substituting the first equation here we get

$T= \frac {4\times 2Q}{W}$

Since it takes 2% of final value to settle and considering 100 rad/s for resonant frequency and taking quality factor of 100 then  

$T=\frac {4\times 2\times 100}{100}= 8 s$