Question

If x, v and a denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period T, then, which of the following does not change with time?

(a) a²T² + 4π²v² 

(b) aT/x

(c) aT + 2πv 

(d) aT/v

Answer 1

(b) : For a simple harmonic motion,
acceleration, a = –ω²x where ω is a constant = 2π/T.

a = - 4π²/T². x ⇒​ aT/x = - 4​π²/T.

The period of oscillation T is a constant.
∴ aT/x is a constant.​