Question

A weakly damped harmonic oscillator of frequency $n_1$ is driven by an external periodic force of frequency $n_2$. When the steady state is reached, the frequency of the oscillator will be

• A. $n_1$
• B. $n_2$
• C. $\frac{n_1+n_2}{2}$
• D. $(n_1+n_2)$

Answer 1

The correct option is B $n_2$

Given,
Frequency of weakly damped harmonic oscillator $=n_1$
Frequency of external periodic force $=n_2$

Steady state is achieved when external force has acted for a sufficiently long time. Therefore, system starts oscillating with the frequency of driving force.
$\therefore$ Frequency of oscillator will be equal to $n_2$.