In a simple harmonic motion of amplitude A, let the instantaneous kinetic energy K be n times the instantaneous potential energy U.
a. (a) Derive, in terms of n, an expression for the displacement x (measured from the mean position) at which this condition holds.
b. (b) Using the result of part (a), find the displacement when n=3.
c. (c) For a block of mass 0.20kg attached to a spring of force constant 150Nm−1 executing SHM with amplitude 0.12m, calculate the kinetic energy and the speed of the block at the displacement obtained in part (b).