The phase difference between the instantaneous velocity and acceleration of a particle executing simple harmonic motion is:
-
0.5π
-
π
-
0.707 π
-
zero
A.
0.5π
The displacement equation of particle executing SHM is
x = a cos ( ωt +Φ) .. (i)
velocity, v = dx/dt = - aω sin (ωt + Φ) .. (ii)
and acceleration,
Fig (i) is a plot of eq (i) with Φ = 0. Fig (ii) shows Eq. (ii) also with Φ = 0 fig (iii) is a plot of Eq (iii) . it should be noted that in the figures the curve of v is shifted (to the left) from the curve of x by one - equate period (T/4).Similarly, the acceleration curve of A is shifted (to the left) by T/4 relative to the velocity curve of v. This implies that velocity is 90o C (0.5 π) out phase with the displacement and the acceleration is 90o C (0.5 π) out of phase with the velocity but 180o π out phase with displacement.
