Question

12. The potential energy of particle moving in S.H.M. is
kar?. If the frequency of the particle is n, the
frequency of oscillation of P.E. is :
(a) n
(b) 2n
(c)n/2
(b) n√2​

Answer 1

Answer:

Given:

Frequency of particle undergoing

SHM is n.

To find:

Frequency of oscillation of Potential Energy.

Concept:

Since the object continuously changes Velocity and experiences different force at different stages of the SHM , the potential energy also oscillate with a particular frequency.

Calculation:

$\large{ \sf{ \blue{PE = \dfrac{1}{2}m { \omega}^{2} {x}^{2}}}}$

$\large{ \sf{ \blue{ = > PE = \dfrac{1}{2}m { \omega}^{2} { \{A \cos( \omega t) \} }^{2}}}}$

$\large{ \sf{ \blue{ = > PE = \dfrac{1}{2}m { \omega}^{2} {A}^{2} { \{ \cos( \omega t) \} }^{2}}}}$

We know a Trigonometric Identity :

${ \cos}^{2} (x) = \dfrac{1 + \cos(2x)}{2}$

$\large{ \sf{ \blue{ = > PE = \dfrac{1}{2}m { \omega}^{2} {A}^{2} \{ \dfrac{1 + \cos(2 \omega t)}{2} \}}}}$

So Potential Energy is Oscillatimg with twice frequency as compared to SHM particle.

So frequency = 2n.