easy way to find phase difference if a particle is showing SHM

1.	easy way to find phase difference if a particle is showing SHM
Answer» Displacement in SHM is given by x = A sin( wt) where A is amplitude, w is angular velocity, t is instantaneous time. Velocity is rate of change of displacement with time. Differentiating displacement with respect to time, we have, V = Aw cos(wt) Phase difference between sin and cos function is 90 degrees or pi/2 radians . Hence phase difference between displacement and velocity is 90 degrees or pi/2 radians. Similarly, acceleration can be obtained by differentiating equation of velocity. Acceleration a = - Aw^2 sin (wt) Hence phase difference between velocity and acceleration is also pi/2. Phase difference between displacement and acceleration is pi radians or 180 degrees. Hope this will clear concept

Answer»

Displacement in SHM is given by x = A sin( wt) where A is amplitude, w is angular velocity, t is instantaneous time.

Velocity is rate of change of displacement with time. Differentiating displacement with respect to time, we have,

V = Aw cos(wt)

Phase difference between sin and cos function is 90 degrees or pi/2 radians . Hence phase difference between displacement and velocity is 90 degrees or pi/2 radians.

Similarly, acceleration can be obtained by differentiating equation of velocity.

Acceleration a = - Aw^2 sin (wt)

Hence phase difference between velocity and acceleration is also pi/2.

Phase difference between displacement and acceleration is pi radians or 180 degrees.

Hope this will clear concept

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