$A$ uniform rod of mass $m$ and length $l$ is suspended about its end. The time period of small angular oscillations is ..........

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 $\text{ s}$)

$A$ particle is performing a linear simple harmonic motion of amplitude $A$. When it is midway between its mean and extreme position,the magnitudes of its velocity and acceleration are equal. What is the periodic time of the motion?

$A$ particle of mass $m$ is executing oscillations about the origin on the $X-$axis. Its potential energy is $U(x) = k|x|^3$,where $k$ is a positive constant. If the amplitude of oscillation is $a$,then its time period $T$ is:

$A$ $U$-tube of uniform bore of cross-sectional area $A$ has been set up vertically with open ends facing up. Now $M$ grams of a liquid of density $d$ is poured into it. The column of liquid in this tube will oscillate with a period $T$ such that

$A$ ring whose diameter is $1 \ m$ oscillates simple harmonically in a vertical plane about a nail fixed at its circumference. The time period will be ....... $s$.