Assertion : Resonance is a special case of fo | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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.

Vedclass · Answer

(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.

Similar Questions

Write the practical examples of resonance.

The amplitude of a damped harmonic oscillator becomes half in $3 \ s$ and will become $1/x$ of the initial amplitude in the next $6 \ s$,where $x$ is:

If the amplitudes of a damped harmonic oscillator at times $t=0, t_1$ and $t_2$ are $A_0, A_1$ and $A_2$ respectively,then the amplitude of the oscillator at a time of $(t_1+t_2)$ is

The amplitude of a damped oscillator becomes half in $1$ minute. The amplitude after $3$ minutes will be $\frac{1}{x}$ times the original. Then $x$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module