The displacement of a particle performing linear S.H.M. is given by y = A [ (t + )] . If at t = 0 , the displacement is y = 2 cm and velocity is 2 cm/s, the value of amplitude A in cm is

Step-by-step solution

Given equation of displacement is y = A [ (t + )] Velocity is given by v = dy dt = -A [ (t + )] At t = 0 , y = 2 A ( ) = 2 At t = 0 , v = 2 -A ( ) = 2 -A ( ) = 2 Squaring and adding the two equations: A^2 ^2( ) + A^2 ^2( ) = (2)^2 + (-2)^2 A^2 = 4 + 4 = 8 A = 2 2 cm Answer: 2 2