In a seconds pendulum,the mass of the bob is $30\, g$. If it is replaced by a $90\, g$ mass,then its time period will be .... $s$.

The bob of a simple pendulum of length $L$ is released from a position of small angular displacement $\theta$. Its linear displacement at time $t$ is ($g =$ acceleration due to gravity).

$A$ hydrometer executes simple harmonic motion when it is pushed down vertically in a liquid of density $\rho$. If the mass of the hydrometer is $m$ and the radius of the hydrometer tube is $r$,then the time period of oscillation is

$A$ small sphere oscillates simple harmonically in a watch glass whose radius of curvature is $1.6 \ m$. The period of oscillation of the sphere is (acceleration due to gravity $g = 10 \ m/s^2$) (in $\pi \ s$)

$A$ simple pendulum of length $l$ is made to oscillate with an amplitude of $45^{\circ}$. The acceleration due to gravity is $g$. Let $T_0 = 2 \pi \sqrt{l / g}$. The time period of oscillation of this pendulum will be

$A$ cylindrical piece of cork of density $\rho$, base area $A$, and height $h$ floats in a liquid of density $\rho_{l}$. The cork is depressed slightly and then released. Show that the cork oscillates up and down simple harmonically with a period $T=2 \pi \sqrt{\frac{h \rho}{\rho_{l} g}}$. (Ignore damping due to viscosity of the liquid).