A particle executes simple harmonic motion with an amplitude of 10 cm. At what distance from the mean position are the kinetic and potential energies equal ?

A = 10cm =0.1m

kinetic energy = mA²w² cos²wt/2 ................1

potential energy = mA²w²sin²wt/2 ..................2

PE = KE           (GIVEN)

so

       tanwt = 1

      sinwt =1/sqrt(2)

now ,  x = Asinwt

            =A/sqrt2= 7cm