Question

During the phenomenon of resonance:

• A. The amplitude of oscillations becomes large
• B. The frequency of oscillations becomes large
• C. The time period of oscillation becomes large
• D. All of the above

Answer 1

The correct option is A The amplitude of oscillations becomes large

Angular frequency of free damped oscillations is given by
${\omega }^{\prime }=\sqrt{{\omega }_0^2-{\gamma }^2}$
When $\gamma <<{\omega }_0$ (i.e weak damping), then ${\omega }^{\prime }\approx {\omega }_0$.
The maximum amplitude of forced oscillations is given by
$A_{max}=\frac{F_0}{2m\gamma \left(\sqrt{{\omega }_0^2-{\gamma }^2}\right)}.....\left(1\right)$
At resonance, $A_{max}=\frac{F_0}{2m\gamma {\omega }_0}$.

Clearly this is the largest value , as for ${\omega }^{\prime }<{\omega }_0$ or ${\omega }^{\prime }>{\omega }_0$, the denominator value of $\left(1\right)$ increases, thus the value of $A_{max}$ decreases.
Thus, during the phenomenon of resonance, the amplitude of oscillation becomes large, because applied frequency is equal to natural frequency.