Question

the phase change of a particle performing SHM between succesive passage through the mean position is​

Answer 1

Answer:

Displacement of the particle executing SHM is given by x=Acoswt

Differentiating it w.r.t. time we get v=

dt

dx

=−Awsinwt

Differentiating it again w.r.t. time we get acceleration as a=

dt

dv

=−Aw

2

coswt

⟹ a=Aw

2

cos(wt+π)

Thus phase difference between displacement and acceleration is π radian.

Explanation:

hope this will help you

Answer 2

The phase change of a particle performing SHM between successive passage through the mean position is given below -

• Simple harmonic motion is a type of periodic motion where the restoring force on the moving object is directly proportional to the magnitude of the object's displacement and acts towards the object's equilibrium position.

• Displacement of the particle executing SHM is given by x = ACosωt ( Where x is the displacement, A is the amplitude, ω is the angular frequency, t is the time.)

Differentiating it with respect to time we get v = dx/dt (Where v is the velocity)

                                                                                  = −Aωsinωt

Differentiating it again with respect to time we get acceleration as a = dv/dt (Where a is the acceleration.)

a = −Aω² Cosωt

a = Aω²C  os(ωt+π)

The difference between the displacement and acceleration is 180°.

Thus phase difference between displacement and acceleration is π radian.