$A$ rod of mass $m$ and length $l$ is suspended from the ceiling with two strings of length $l$ as shown. When the rod is given a small push in the plane of the page and released,the time period is $T_1$. When the rod is given a push perpendicular to the plane,the time period of oscillation is $T_2$. The ratio $\frac{T_1^2}{T_2^2}$ is

Two light identical springs of spring constant $k$ are attached horizontally at the two ends of a uniform horizontal rod $AB$ of length $l$ and mass $m$. The rod is pivoted at its centre $O$ and can rotate freely in a horizontal plane. The other ends of the two springs are fixed to rigid supports as shown in the figure. The rod is gently pushed through a small angle $\theta$ and released. The frequency of the resulting oscillation is

$A$ ring of diameter $2 \ m$ oscillates as a compound pendulum about a horizontal axis passing through a point at its rim. It oscillates such that its centre moves in a plane which is perpendicular to the plane of the ring. The equivalent length of the simple pendulum is .... $m$

If a body is released into a tunnel dug across the diameter of the Earth,it executes simple harmonic motion with a time period of:

The relation between the force ($F$ in newton) acting on a particle executing simple harmonic motion and the displacement of the particle ($y$ in metre) is $500 F + \pi^2 y = 0$. If the mass of the particle is $2 \text{ g}$, the time period of oscillation of the particle is (in $\text{ s}$)

$A$ rectangular block of mass $m$ and area of cross-section $A$ floats in a liquid of density $\rho$. If it is given a small vertical displacement from equilibrium,it undergoes simple harmonic motion with a time period $T$. Then: