A forced oscillator is acted upon by a force, `F=F_(0)sinomegat`. The amplitude of the oscillator is given by `A=(55)/(sqrt((2omega^(2)-36omega+9)))`
What is the resonance angular freuqnecy (in rad/s)?

Options

A. 36
B. 18
C. 9
D. 2

Answer

C

Explanation

`A = 55/(sqrt((2omega^(2) - 36omega + 9)))`
At resonace, the amplitude is maximum. This is possible
if `sqrt(2 omega^(2) - 36 omega + 9) ` is minimum.
For this , `d/(d omega) [2 omega^(2) - 3 6 omega + 9] ` must be = 0
` :. 4 omega - 36 = 0 " or " omega = 9 `