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?

In Simple Harmonic Motion (SHM), the acceleration $a$ is related to displacement $x$ by the equation:
$$a=-{\omega }^{2}x$$
where $\omega =\frac{2\pi }{T}$ is the angular frequency.Taking the magnitude:
$$\frac{|a|}{x}={\omega }^2={\left(\frac{2\pi }{T}\right)}^2=\frac{4{\pi }^2}{T^2}$$
Rearranging this:
$$\frac{a{T}^2}{x}=-4{\pi }^2$$
Since $T$ and $\omega$ are constants for a given SHM, the ratio $\frac{a{T}^2}{x}$ remains constant over time.