A particle performs simple harmonic motion with amplitude A . Its speed is increased to three times at an instant when its displacement is 2 A 3 . The new amplitude of motion is n A 3 . The value of n is _____.

Step-by-step solution

Speed in SHM in terms of displacement is given by, v = ω A 2 - x 2 . at x = 2 A 3 , we get v = ω A 2 - 2 A 3 2 = 5 A ω 3 Let the new amplitude be = A ' Then, v ' = 3 v ⇒ ω A ' 2 - 2 A 3 2 = 5 A ω ⇒ A ' = 7 3 A Therefore, n = 7 .