$A$ particle executes $SHM$ in a line $4 \, cm$ long. Its velocity when passing through the centre of the line is $12 \, cm/s$. The period will be ..... $s$. (in $.047$)

$A$ ring is suspended from a point $S$ on its rim as shown in the figure. When displaced from equilibrium,it oscillates with a time period of $1 \, s$. The radius of the ring is ..... $m$ (take $g = \pi^2$).

$A$ ball is rolling without slipping in a spherical shallow bowl (radius $R$) as shown in the figure and is executing simple harmonic motion. If the radius of the ball is doubled,then the time period of oscillation

$A$ large horizontal surface moves up and down in $S.H.M.$ with an amplitude of $1 \, cm$. If a mass of $10 \, kg$ placed on the surface is to remain continuously in contact with it,the maximum frequency of $S.H.M.$ will be .... $Hz$.

$A$ long stiff uniform wire of length $\ell$ is suspended from one end. The time period of oscillations of the wire is $T$. If the wire is now bent into a circle and suspended from a knife edge so that it can oscillate freely in the plane of the ring,its time period will be

The ends of a rod of length $l$ and mass $m$ are attached to two identical springs. The rod is free to rotate about its centre $O$. The rod is depressed slightly at end $A$ and released. The time period of the resulting oscillation is