Question

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 $cos\omega t$ $(\omega?\omega_0)$ is applied to the oscillator. The time displacement of the oscillator will be proportional to

• A. $\frac{m}{\omega^{2}_{0}-\omega^{2}}$
• B. $\frac{1}{m\left(\omega ^{2}_{0}-\omega ^{2}\right)}$
• C. $\frac{1}{m\left(\omega ^{2}_{0}+\omega ^{2}\right)}$
• D. $\frac{m}{\omega^{2}_{0}+\omega^{2}}$

Answer 1

Answer: (B)

$\frac{1}{m\left(\omega ^{2}_{0}-\omega ^{2}\right)}$

Answer 2

For forced oscillations, the displacement is given by $x = A\, sin\left(?t + \phi\right)$ with $A = \frac{F _{0}/m}{\omega^{2}_{0}-\omega^{2}}$