Question

A forced oscillator is acted upon by a force F = F₀ sin ωt. The amplitude of oscillation is given by $\frac{55}{\sqrt{2\omega^{2}-36\omega+9}}$. The resonant angular frequency is(a) 2 unit(b) 9 unit(c) 18 unit(d) 36 unit

Answer 1

2 unit is the answer

Answer 2

Given that,

A forced oscillator is acted upon by a force :

$F=F_o\sin \omega t$

Amplitude of oscillation, $A=\dfrac{55}{\sqrt{2\omega ^2-36\omega +9} }$

To find,

The resonant angular frequency.

Solution,

At resonance, the amplitude of oscillation is maximum. So,

$2\omega^2-36\omega+9=0$

For maximum,

$\dfrac{d\omega}{dt}=0\\\\\dfrac{d(2\omega^{2}-36\omega+9)}{dt}=0\\\\4\omega-36=0\\\\\omega=9$

So, the resonant angular frequency is 9 units.

Learn more,

Forced oscillator

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