The ratio between kinetic and potential energies of a body executing simple harmonic motion, when it is at a distance of 1 N of its amplitude from the mean position is

Step-by-step solution

The kinetic energy KE = 1 2 m ^2 [ a ^2- ( a N )^2 ] The potential energy PE = 1 2 m ^2 a ^2 ~N ^2 From the Eqs. (i) and (ii), we get aligned KE PE & = 1 2 m ^2 [a^2- ( a N )^2 ] 1 2 m ^2 a^2 N^2 & = a^2- a^2 N^2 a^2 N^2 = a^2 N^2 (N^2-1 ) a^2 N^2 =N^2-1 aligned