Question

During SHM, K.E. of particle in SHM varies with frequency of 176 Hz. Find the frequency of SHM of the particle.

• A. 352 Hz
• B. 176 Hz
• C. 88 Hz
• D. 44 Hz

Hint:

In SHM, the kinetic energy oscillates at twice the frequency of the particle's oscillation. This is because K.E. depends on the square of velocity, which oscillates twice per cycle of the SHM.

Answer 1

The Correct Option is C

Step 1: Understanding the relationship between K.E. and frequency.
The kinetic energy (K.E.) of a particle in Simple Harmonic Motion (SHM) is given by the formula: \[ K.E. = \frac{1}{2} m \omega^2 A^2 \cos^2(\omega t) \] where \( m \) is the mass of the particle, \( \omega \) is the angular frequency, \( A \) is the amplitude of oscillation, and \( t \) is the time. The frequency \( f \) is related to angular frequency by: \[ \omega = 2 \pi f \]
Step 2: Frequency of K.E. variation.
It is given that the K.E. varies with a frequency of 176 Hz. This implies that the frequency of the oscillations of the K.E. is twice the frequency of SHM, because the K.E. in SHM oscillates twice per cycle of the motion (once when the particle is moving in the positive direction and again when it moves in the negative direction). \[ f_{\text{K.E.}} = 2 f_{\text{SHM}} \]
Step 3: Solve for SHM frequency.
Given that \( f_{\text{K.E.}} = 176 \) Hz, we can solve for \( f_{\text{SHM}} \): \[ 176 = 2 f_{\text{SHM}} \] \[ f_{\text{SHM}} = \frac{176}{2} = 88 \, \text{Hz} \] Thus, the frequency of SHM of the particle is 88 Hz.