A particle of mass m executes SHM with amplitude a and frequency n. What is the average kinetic energy of the particle during its motion from the position of equilibrium to the end?

Explanation

KE in the mean position = `1/2ma^(2)w^(2)`
`=1/2ma^(2)(2pin)^(2)`
`=2pi^(2)ma^(2)n^(2)`
KE at the end = 0
`therefore` Average kinetic energy = `(0+2pi^(2)ma^(2)n^(2))/2=pi^(2)ma^(2)n^(2)`