If the temperature of a pendulum with time period $T$ is increased by $\Delta \theta$,the change in the time period of the pendulum is .......

$A$ simple pendulum with a bob of mass $40 \ g$ and charge $+2 \ \mu C$ makes $20$ oscillations in $44 \ s$. $A$ vertical electric field of magnitude $4.2 \times 10^4 \ NC^{-1}$ pointing downward is applied. The time taken by the pendulum to make $15$ oscillations in the electric field is (acceleration due to gravity $= 10 \ ms^{-2}$) (in $s$)

$A$ simple pendulum,suspended from the ceiling of a stationary van,has time period $T$. If the van starts moving with a uniform velocity,the period of the pendulum will be

$A$ disc of mass $m$ and radius $R$ is attached to the ceiling with the help of two ropes of length $l$. Find the time period of small oscillations of the disc in the plane of the disc.

The path length of oscillation of a simple pendulum of length $1 \,m$ is $16 \,cm$. Its maximum velocity is (Take $g = \pi^2 \,m/s^2$).

The bob of a pendulum of length $l$ is pulled aside from its equilibrium position through an angle $\theta$ and then released. The bob will then pass through its equilibrium position with speed $v$,where $v$ equals