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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 do not
change with time?

A
$$aT+2\pi v$$
B
$$\dfrac{aT}{v}$$
C
$$vT$$
D
$$a^2T^2+4\pi^2 v^2$$
E
$$aT$$
Solution
Verified by Toppr

Correct option is A. $$\dfrac{aT}{v}$$
$$\because$$ In option $$(a),\dfrac{aT}{v}=\dfrac{\dfrac{m}{s^2}\times s}{\left(\dfrac{m}{s}\right)}=\dfrac{m\times s^2}{m\times s^2}=[M^0L^0T^0]$$
So, according to the result above relation does not depend on time

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