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

Answer

A

Explanation

For a simple harmonic motion, acceleration, `a=-omega^(2)x` where `omega=(2pi)/(T)` is a constant.
`therefore a=-(4pi^(2))/(T^(2))xor(aT)/(x)=-(4pi^(2))/(T)`
`therefore (aT)/(x)` is a constant.