A particle is vibrating in S.H.M. with an amplitude of 4 ~cm . At what displacement from the equilibrium position is its energy half potential and half kinetic?

Step-by-step solution

aligned K.E & = 1 2 m ^2 ( ~A ^2- x ^2 ) and P.E & = 1 2 ~m ^2 x ^2 T . E & = K E + P E & = 1 2 ~m ^2 ( ~A ^2- x ^2 )+ 1 2 ~m ^2 x ^2 & = 1 2 ~m ^2 ~A ^2 & Given: K E = P E , A ^2 & - x ^2= x ^2 A ^2 & =2 x ^2 X & = A ^2 2 = A 2 x & = 4 2 =2 2 ~cm aligned