A particle executes a linear S.H.M of amplitude 3 cm. When it is at 1 cm from the mean position, the magnitude of its velocity is half that of its acceleration at the point. The maximum velocity is

Step-by-step solution

Amplitude A = 3 cm. Magnitude of velocity at distance x from the mean position is v = A^2 - x^2 . Magnitude of acceleration at distance x is a = ^2 x . Given that at x = 1 cm, v = 1 2 a . 3^2 - 1^2 = 1 2 ^2 (1) 8 = 1 2 ^2 = 2 8 = 4 2 rad/s. Maximum velocity is v_ = A . v_ = 3 4 2 = 12 2 cm/s. Answer: 12 2 cm/s