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


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Answer 1

$\huge\bigstar\underline\pink{Answer}$

★ Option b is correct ✔️

★ acceleration = w²x

w = 2π/T

★ aT/x = w²xT/x =(2π/T)²xT/x = 4π²/T

which is constant term, as time period is constant.

$\huge\red{\ddot{\smile}}$

Answer 2

Explanation :- We have to check all four option there will be error . But i will explain only correct option .

Independently x, v, and a are indenpendently

(b) aT/x = xω² T/x

• ∵ a = ω²x

4π²/T² × T = 4π ²/T = constant .

Hence, aT/x does not change with time .

• Hence, Option (B) is correct .