Question

If the particle starts is its Motion from mean position the phase difference between displacement acceleration is

Answer 1

Standard equation of wave motion is y = Asinωt, when wave starts motion from at mean position.
y = A sinωt
Now, differentiate with respect to t,
dy/dt = Aω cosωt = Aωsin(ωt + π/2)
dy/dt =velocity of particle = Aωsin(ωt + π/2)

again, differentiate with respect to t ,
d²y/dt² = -Aω²sinωt = Aω²sin(ωt + π)
acceleration of particle = d²y/dt² = Aω²sin(ωt + π)

Here it is clear that phase of phase constant of velocity is π/2 and acceleration is π. Hence, phase difference between acceleration and velocity is (π - π/2) = π/2
So, answer is π/2