$A$ block of mass $m$ rests on a platform. The platform is given up and down $SHM$ with an amplitude $d$. What is the maximum frequency so that the block never leaves the platform?

$A$ body of mass $100 \ g$ is tied to a spring of spring constant $8 \ N/m$,while the other end of the spring is fixed. If the body moves in a circular path on a smooth horizontal surface with a constant angular speed of $8 \ rad/s$,then the ratio of the extension in the spring to its natural length will be: (in $:1$)

The time period of oscillation for the given combination will be:

$A$ force of $6.4 \,N$ stretches a vertical spring by $0.1 \,m$. If it were to oscillate with a period of $\frac{\pi}{4} \,s$, then the mass that is to be suspended from the spring is:

If the period of oscillation of mass $m$ suspended from a spring is $2 \, s$,then the period of mass $4m$ will be .... $s$.

$A$ block of mass $1 \; kg$ is fastened to a spring with a spring constant of $50 \; N m^{-1}$. The block is pulled to a distance $x = 10 \; cm$ from its equilibrium position at $x = 0$ on a frictionless surface and released from rest at $t = 0$. Calculate the kinetic,potential,and total energies of the block when it is $5 \; cm$ away from the mean position.