The phase difference between displacement and velocity of a particle in simple harmonic motion is

Step-by-step solution

The displacement of a particle in simple harmonic motion is given by x(t) = A ( t + ) . The velocity of the particle is the time derivative of displacement, v(t) = dx dt = A ( t + ) . Using the trigonometric identity ( ) = ( + /2) , the velocity can be written as v(t) = A ( t + + /2) . Comparing the phases of displacement and velocity, the phase of displacement is t + and the phase of velocity is t + + /2 . The phase difference is ( t + + /2) - ( t + ) = /2 rad . Answer: / 2 ~rad