Where is the maximum velocity in SHM.

The position co-ordinates of a particle moving in a $3D$ coordinate system is given by

$x=a\cos \mathrm{\omega }\mathrm{t}$

$y=a\sin \omega t$

and $z=a\omega t$

The speed of the particle is:

One end of a spring of force constant $k$ is fixed to a vertical wall and the other to a block of mass $m$ resting on a smooth horizontal surface. There is another wall at a distance $x_0$, from the block. The spring is then compressed by $2x_0$ and released. The time taken by the block to strike the other wall is

In case of a simple harmonic motion, if the velocity is plotted along the $X$ -axis and the displacement (from the equilibrium position) is plotted along the $Y$ -axis, the resultant curve happens to be an ellipse with the ratio:
$\frac{\text{ major axis }\left(\text{along }X\right)}{\text{ minor axis }\left(\text{along }Y\right)}=20\pi$

What is the frequency of the simple harmonic motion?

The motion of a mass on a spring, with spring constant $K$ is as shown in figure.

The equation of motion is given by, $x\left(t\right)=A\sin \omega t+$$B\cos \omega \mathrm{t}$ with $\omega =\sqrt{\frac{K}{m}}$.
Suppose that at time $t=0,$the position of mass is $x\left(0\right)$ and velocity $v\left(0\right),$ then its displacement can also be represented as $x\left(t\right)=C\cos (\omega t-\varphi ),$ where $C$ and $\varphi$ are