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.

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opudodennis opudodennis · Answer 1 · 2020-03-08T11:31:08+01:00

Answer:

8 s

Explanation:

Damping factor, F is given by

[tex]F=\frac {1}{2Q}[/tex] where Q is quality factor

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

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

[tex]T= \frac {4\times 2Q}{W}[/tex]

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

[tex]T=\frac {4\times 2\times 100}{100}= 8 s[/tex]