Question

A particle executes simple harmonic motion with a frequency ν. The frequency with which the kinetic energy oscillates is
(a) ν/2
(b) ν
(c) 2ν
(d) zero

Answer 1

Answer ⇒ Option (c). 2v

Explanation ⇒ The Frequency of the Potential energy or the Kinetic Energy is always double to that of the displacement, velocity or Force and Acceleration in case of the Simple Harmonic Motion.

Since, the frequency of the Particle executing Simple Harmonic Motion is v, therefore,  frequency of the Kinetic Energy or that of the Potential energy = 2v.

Physics also asks the Reason. You can learn the given result, but for reason?

Reason ⇒ Time period is the total time taken to reach the same position from where it is started and in the same direction.

Now, For Kinetic Energy and Potential energy, meaning of direction s irrelevant and none of use, since they are scalar quantity. Thus, only magnitude is there. Now, If the Particle starts from mean position it will repeats it value after T/2 (In Case of Velocity it is T/4).

Now, Frequency = 1/T'  

Substituting T' = T/2

v' = 2/T

Ans, Frequency of velocity,

v = 4/T

∴ v' = 2v

Hence, Option (c). is correct.

Hope it helps.