A mass is suspended from a vertical spring which is executing SHM of frequency $5 \mathrm{Hz}$. The spring is unstretched at the highest point of oscillation. The maximum speed of the mass is (acceleration due to gravity, $g=10 \mathrm{m} {\mathrm{s}}^{-2}$),

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 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?

A ball of mass $\left(m\right) 0.5 \mathrm{kg}$ is attached to the end of a string having length $\left(L\right)$ $0.5 \mathrm{m}$. The ball is rotated on a horizontal circular path about the vertical axis. The maximum tension that the string can bear is $324 \mathrm{N}$. The maximum possible value of angular velocity of ball $(\text{in} \mathrm{radian} {\mathrm{s}}^{-1})$ is,

The mass $M$ shown in the figure oscillates in simple harmonic motion with amplitude $A$. The amplitude of the point $P$ is,