NCERT Class 11 Physics Solutions: Chapter 14 – Oscillations-Part 16

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Question 14.22:

Show that for a particle in linear SHM the average kinetic energy over a period of oscillation equals the average potential energy over the same period.

Answer:

The equation of displacement of a particle executing SHM at an instant t is given as:

Where,

Amplitude of oscillation

Angular frequency

The velocity of the particle is:

The kinetic energy of the particle is:

The potential energy of the particle is:

For time period the average kinetic energy over a single cycle is given as:

And, average potential energy over one cycle is given as:

It can be inferred from equations that the average kinetic energy for a given time period is equal to the average potential energy for the same time period.