Question

If the particle starts it's motion from mean position the phase different between displacement and acceleration is ....
A)2π Rad B)π/2 Rad C)π Rad D) π/4 Rad

Answer 1

π/2rad.
Hence phase difference between displacement and velocity is 90 degrees or pi/2 radians. ... 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

Answer : (B) π/2 rad

Explanation : as you know, standard equation of wave is y = Asin(ωt ± Ф)
Now, differentiate with respect to x ,
dy/dt = Aωcos(ωt ± Ф) = Aωsin(π/2 + ωt ± Ф)
dy/dt = velocity of particle = Aωsin(π/2 + ωt ± Ф)

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

you can see that phase difference between acceleration and velocity is ΔФ = π - π/2 = π/2 rad