Q.Define forced oscillation. Give an example.

Resonance in Forced Oscillations

Every oscillator has a natural frequency at which it vibrates when disturbed and left alone. For a simple pendulum this is set only by its length, $\nu_0 = \dfrac{1}{2\pi}\sqrt{\dfrac{g}{L}}$; for a spring-mass system $\nu_0 = \dfrac{1}{2\pi}\sqrt{\dfrac{k}{m}}$. When an external periodic driving force of frequency $\nu_d$ is applied, the system settles into oscillation at the driving frequency $\nu_d$ — this is a forced (driven) oscillation.

The amplitude of the forced oscillation depends sharply on how close the driving frequency is to the natural frequency. Resonance is the condition

at which the driven system absorbs energy from the driver most efficiently and oscillates with maximum amplitude. Away from this match, the response is much smaller; the closer $\nu_d$ is to $\nu_0$, the larger the steady-state amplitude (in the absence of damping the amplitude would grow without bound at exact resonance). …