Question

Assertion :Resonance is a special case of forced vibration in which the natural frequency of vibration of the body is the same as the impressed frequency of external periodic force and the amplitude of forced vibration is maximum. Reason: The amplitude of forced vibrations of a body increases with an increase in the frequency of the externally impressed periodic force.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

Answer: (C)

The amplitude become large when the frequency of the driving force $\left(\omega \right)$ is near the natural frequency of oscillation or when $\omega ={\omega }_0$. This frequency is known as resonance frequency. Amplitude of oscillation for a forced, damped oscillator is

$A=\frac{f_{0/m}}{\sqrt{({\omega }^2-{\omega }_0^2)+(b\omega /m{)}^2}}$
where $b$ is constant related to the strength of the resistive force, ${\omega }_0=\sqrt{k/m}$ is natural frequency of undamped oscillator $(b=0)$.