A particle performs S.H.M. with amplitude 'A'. Its speed is tripled at the instant when it is at a distance of 2 ~A 3 from the mean position. The new amplitude of the motion is

Step-by-step solution

Kinetic energy of a particle performing S.H.M. is given by k= 1 2 m ² (A²-x² ) When x= 2 3 A , k = 1 2 ~m ² ( ~A ²- 4 9 ~A ² )= 1 2 ~m ² ~A ² 5 9 If the velocity is tripled, its kinetic energy will become 9 times. The new kinetic energy will be k^ = 1 2 m ² A² 5 The potential energy p= 1 2 m ² ( 2 3 A )²= 1 2 m ² A² 4 9 If A^ is the new amplitude then the total energy e is given by E= 1 2 m ² A^ 2 Also, E=P+k^ 1 2 m ² A^ 2 = 1 2 m ² A² 4 9 + 1 2 m ² A² 5 A^ 2 = ( 4 9 +5 ) A² A^ = 7 3 A