Question

If $x,v$ and $a$ denotes 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. $a^2{T}^2+4{\pi }^2{v}^2$
• B. $aT/x$
• C. $aT+2\pi v$
• D. $aT/v$

Answer 1

The correct option is B $aT/x$

We know that,
$a=-{\omega }^{2}x$
($\because$ particle executes SHM)
Muliplying on both sides with $\frac{T}{x}$ we get :
$\frac{aT}{x}=-{\omega }^{2}T$
$(\because \omega =\frac{2\pi }{T})$
$\Rightarrow \frac{aT}{x}=-\frac{4{\pi }^2}{T}=$ constant

Since, the velocity of the particle is changing at every instant, therefore, every option other then option $\left(b\right)$ changes with the time.

Hence, option $\left(b\right)$ is the correct answer.