A forced oscillator is acted upon by a force $F = F_{0} \sin ω t$ . The amplitude of oscillation is given by $\frac{55}{\sqrt{2 ω^{2} - 36 ω + 9}}$ . The resonant angular frequency is

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36 units

9 units

2 units

18 units

answer is B.

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Detailed Solution

$\begin{array}{l} At resonance, amplitude of oscillation is maximum \\ \Rightarrow 2 ω^{2} - 36 ω + 9 is minimum \\ Differentiating wrt ω and equating to zero gives, \\ \Rightarrow 4 ω - 36 = 0 \\ \Rightarrow ω = 9 \end{array}$

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