Q. 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 $\cos{\omega t(\omega \neq \omega_{0})}$ is applied to the oscillator. The time displacement of the oscillator will be proportional to
A) $\frac{m}{\omega_{0}^{2} - \omega^{2}}$
B) $\frac{1}{m(\omega_{0}^{2} - \omega^{2})}$
C) $\frac{1}{m(\omega_{0}^{2} + \omega^{2})}$
D) $\frac{m}{\omega_{0}^{2} + \omega^{2}}$
Explanation
(b) For forced oscillation,
$x = x_{0}\sin{(\omega t + \phi)}$ and $F = F_{0}\cos{\omega t}$
$where,\ x_{0} = \frac{F_{o}}{m(\omega_{o}^{2} - \omega^{2})} \propto \frac{1}{m(\omega_{o}^{2} - \omega^{2})}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.