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

Answer

A

Explanation

For a simple harmonic oscillator,
`a= -omega^(2)x= -(4pi^(2))/(T^(2))x therefore (aT)/(x)= -(4pi^(2))/(T)`
`because` T is constant, `(4pi^(2))/(T)` is constant
`therefore (aT)/(x)` is a constant. It does not change with time.
Other terms involve v, which change with time.