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 does not change with time?

• A. $a^2 T^2 +4 \pi^2 v^2$
• B. $\frac{a T}{x}$
• C. $aT + 2 \pi v$
• D. $\frac{a T}{v}$

Answer 1

Answer: (B)

$\frac{a T}{x}$

Answer 2

For a particle executing simple harmonic motion, acceleration, $a = - \omega^2 x$ where $\omega = \frac{2 \pi}{T}$ $a = - \frac{4 \pi^2}{T^2} x$ or $\frac{aT}{x} = - \frac{4 \pi^2}{T}$ The period of oscillation T is a constant. $\therefore \:\: \frac{aT}{x}$ is a constant.