Question

find phase difference between displacement ,velocity and acceleration of a particle in simple harmonic motion???

Answer 1

Displacement in SHM is given by x = A sin( wt) where A is amplitude, w is angular velocity, t is instantaneous time. ... Hence phase difference between velocity and acceleration is also pi/2. Phase difference between displacement and acceleration is pi radians or 180 degrees.

Answer 2

Y=a sin(wt+ø)

on differentiation,

v=aw cos(wt + ø)

again differentiation u will get,

a= - aw² sin(wt+ø)

now take the minus sign inside as π

a= aw²sin(wt + ø + π)

So phase difference between displacement and acceleration will be----->

= wt + ø + π —{ wt + ø}

= wt + ø + π - wt - ø

= π

hope this answer helpful u