Question

Show that for a particle executing SHM the velocity and displacement have phase difference π/2

Answer 1

we know ,

trajectory of particle in simple harmonic motion is y = Asin (wt +_kx) ------(1)

differentiate with respect to t

dy/dt = wAcos (wt +_kx )

we know change in displacement per unit time is called velocity .

so,

v = wA.sin (wt +_kx + pi/2)-----------(2)

compare in phase of equation (1) and (2)


we see phase difference between velocity and displacement is pi/2