Question

A block of mass m is attached to a spring of spring constant k and has a natural frequency ${\omega }_0$. An external force $F\left(t\right)$ proportional to $cos\omega t(\omega \ne {\omega }_0)$ 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. $\frac{m}{{\omega }_0^2+{\omega }^2}$

Answer 1

The correct option is B $\frac{1}{m({\omega }_0^2-{\omega }^2)}$

For forced oscillation, the time displacement at any instant is given by
$x=\frac{F_0}{m({\omega }_0^2-{\omega }^2)}cos\omega t,x\propto \frac{1}{m({\omega }_0^2-{\omega }^2)}$