Question

3) Show that in a S.H.M. the phase difference between displacement and velocity is pi/2,
and between displacement and acceleration is pi.
​

Answer 1

Answer:

SHM is represented by x=Asinωt

Then, the velocity and acceleration after differentiation will be

v=Aωcosωt

a=−Aω

2

sinωt

Now, we see displacement is in sinωt & velocity is in cosωt

⇒ Phase difference between x & v=π/2 rad

Similarly, we see velocity in cosωt & acceleration in sinωt

⇒ Phase difference between v & a=π/2rad

Thus, we can conclude that the phase difference between x & a=π rad.