Question
Show that for a particle in linear simple harmonic motion, the average kinetic energy over a period of oscillation is half the total energy.
Solution
Let a particle of mass m execute simple harmonic motion with frequency ω. Let a be the amplitude of vibration.
The position of particle at any instant during simple harmonic motion is given by,
Now the average kinetic energy of particle over complete cycle is,
Hence proved.
The position of particle at any instant during simple harmonic motion is given by,
Now the average kinetic energy of particle over complete cycle is,
Hence proved.
