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?

Options

A. `(aT)/(v)`
B. `aT+2piv`
C. `(aT)/(x)`
D. `a^(2)T+4pi^(2)v^(2)`

Answer

C

Explanation

`(aT)/(x)=(omega^(2)xT)/(x)=omega^(2)T=(4pi^(2))/(T^(2))T" "(becauseomega=(2pi)/(T))`
`=(4pi^(2))/(T)=`constant.