A particle starts oscillating simple harmonically from its mean position with time period ' T '. At time t= T 6 , the ratio of the potential energy to kinetic energy of the particle is [ 30^ = 60^ =0 5, 30^ = 60^ = 3 / 2 ]

Step-by-step solution

The displacement for simple harmonic motion from the mean position is x = A ( t) , where = 2 T . The potential and kinetic energies are given by PE = 1 2 m ^2 A^2 ^2( t) and KE = 1 2 m ^2 A^2 ^2( t) respectively. The ratio simplifies to PE KE = ^2( t) ^2( t) = ^2( t) . At time t = T/6 , the phase angle is t = 2 T T 6 = 3 . Since ( /3) = 3 , the ratio becomes PE/KE = ( 3 )^2 = 3 . The potential to kinetic energy ratio is therefore 3:1 .