Assertion : Resonance is a special case of fo | vedclass

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(C) The $Assertion$ is correct. Resonance occurs when the driving frequency $(\omega)$ equals the natural frequency $(\omega_{0})$ of the system,resul

Vedclass · Accepted Answer

If the Assertion is correct but Reason is incorrect.

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(C) The $Assertion$ is correct. Resonance occurs when the driving frequency $(\omega)$ equals the natural frequency $(\omega_{0})$ of the system,resulting in maximum amplitude.The $Reason$ is incorrect. The amplitude of forced vibrations does not simply increase with the frequency of the external force. Instead,the amplitude follows a resonance curve; it increases as the driving frequency approaches the natural frequency and decreases as it moves away from it.The amplitude of oscillation for a forced,damped oscillator is given by:$A = \frac{F_{0} / m}{\sqrt{(\omega^{2} - \omega_{0}^{2})^{2} + (b \omega / m)^{2}}}$where $b$ is the damping constant and $\omega_{0} = \sqrt{k / m}$ is the natural frequency. As $\omega$ approaches $\omega_{0}$,the denominator decreases,causing the amplitude $A$ to reach its maximum value.

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