A particle is executing simple harmonic motion with an amplitude A . What is the phase difference between its velocity and acceleration at the instant when its displacement is x = A 2 ?

Step-by-step solution

In simple harmonic motion, the equations for displacement, velocity, and acceleration can be written as: x = A ( t + ) v = dx dt = A ( t + ) = A ( t + + 2 ) a = dv dt = -A ^2 ( t + ) = A ^2 ( t + + ) The phase of the velocity is ( t + + 2 ) and the phase of the acceleration is ( t + + ) . The phase difference between velocity and acceleration is: = ( t + + ) - ( t + + 2 ) = 2 radians This phase difference is a constant value that depends only on the mathematical relationship between the kinematic variables. It is e