In forced oscillations displacement equation is x(t) = Acos( $ω_{d} t + θ$ ) then amplitude ‘A’ vary with forced angular frequency $ω_{d}$ and natural angular frequency ‘ $ω$ ’ as (b = damping constant)

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$\frac{F}{{mω}^{2}}$

$\frac{F}{m (ω^{2} - ω_{d}^{2})}$

$\frac{F}{{\{m (ω_{d}^{2} b^{2}) + (ω^{2} - ω_{d}^{2})\}}^{1 / 2}}$

$\frac{F}{{\{m^{2} {(ω^{2} - ω_{d}^{2})}^{2} + ω_{d}^{2} b^{2}\}}^{1 / 2}}$

answer is B.

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Detailed Solution

The amplitude "A" is a function of the external periodic force frequency and the natural
frequency $ω_{0}$
$A = \frac{F_{0}}{m {[{(ω_{0}^{2} - ω_{e}^{2})}^{2} + ω_{e}^{2} {(\frac{b}{m})}^{2}]}^{\frac{1}{2}}}$

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