A particle starts oscillating simple harmonically from its equilibrium position with time period 'T'. What is the ratio of potential energy to kinetic energy of the particle at time t= T 12 ? ( ( 6 )= 1 2 )

Step-by-step solution

For SHM, aligned & P.E. = 1 2 m ^2 x^2 ...(i) & and K.E. = 1 2 m ^2 (A^2-x^2 )...(ii) aligned Given t = T 12 aligned x & =A t=A 2 T t x & =A 2 T T 12 & =A ( 6 ) & = A 2 ...(iii) aligned Substituting equation (iii) in equation (i), aligned P.E. & = 1 2 ~m ^2 ( ~A ^2 4 ) & = m ^2 ~A ^2 8 aligned Substituting equation (iii) in equation (ii), aligned K.E. & = 1 2 ~m ^2 ( ~A ^2- A ^2 4 ) & = 1 2 ~m ^2 ( 3 ~A ^2 4 ) P.E. K.E. & = 1 2 m ^2 A^2 1 4 1 2 m ^2 A^2 3 4 = 1 3 aligned