A particle of mass m is attached to a spring (of spring constant k) and has a natural angular frequency ${\omega _0}$ - An external force $F (t)$ proportional to $\cos \omega \,t((\omega \ne {\omega _0})$ is applied to the oscillator. The time displacement of the oscillator will be proportional to
AIEEE 2004, Medium
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(b) For forced oscillation,
$x = {x_0}\sin (\omega t + \phi )$ and $F = {F_0}\cos \omega \,t$
where, ${x_0} = \frac{{{F_o}}}{{m\,(\omega _o^2 - {\omega ^2})}} \propto \frac{1}{{m(\omega _o^2 - {\omega ^2})}}.$
$x = {x_0}\sin (\omega t + \phi )$ and $F = {F_0}\cos \omega \,t$
where, ${x_0} = \frac{{{F_o}}}{{m\,(\omega _o^2 - {\omega ^2})}} \propto \frac{1}{{m(\omega _o^2 - {\omega ^2})}}.$
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