Question

In SHM if a particle oscillates with frequency $\upsilon$, then find the frequency of oscillation of its kinetic energy.

• A. $\upsilon$
• B. $\upsilon$/2
• C. 2$\upsilon$
• D. Zero

Answer 1

The correct option is C 2$\upsilon$

$\text{Given:-}$ Frequency = v

$\text{To find:-}$ Fequency with which its kinetic energy oscillates

$\text{Solution:-}$

Kinetic energy of the particle executing simple harmonic motion is given by,

K.E = $\frac{1}{2}m{v}^2$

$=\frac{1}{2}m{\omega }^2{A}^{2}co{s}^{2}2\pi vt$

$=Eco{s}^2\omega t=E\left[\frac{1+cos4\pi vt}{2}\right]$

$=\frac{E}{2}+\frac{Ecos2\pi \left(2v\right)t}{2}$

The first term is constant and second term is oscillating having frequency 2v

Thus, the frequency of oscillation of kinetic energy is 2v.

$\text{Hence the correct option is C}$