$A$ particle moving along the $X$-axis executes simple harmonic motion. The force acting on it is given by: (Where $A$ and $K$ are positive constants)

$A$ body is oscillating in simple harmonic motion according to the equation $x = 6 \cos \left(2 \pi t + \frac{\pi}{3}\right) \ m$. The magnitude of the acceleration (in $m/s^2$) of the body at $t = 1 \ s$ is:

Two simple harmonic motions of angular frequency $300 \ rad/s$ and $3000 \ rad/s$ have the same amplitude. The ratio of their maximum accelerations is

If a simple harmonic oscillator has a displacement of $0.02\, m$ and an acceleration equal to $2.0\, m\, s^{-2}$ at any time,the angular frequency of the oscillator is equal to .... $rad\, s^{-1}$.

Two simple harmonic motions of angular frequency $100 \, rad \, s^{-1}$ and $1000 \, rad \, s^{-1}$ have the same displacement amplitude. The ratio of their maximum acceleration is

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?