$A$ seconds pendulum is placed in a space laboratory orbiting round the Earth at a height $3R$ from the Earth's surface. The time period of the pendulum will be ($R =$ radius of Earth).

The average speed of the bob of a simple pendulum oscillating with a small amplitude $A$ and time period $T$ is

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).

If a simple pendulum is released from the given position,find the velocity of the bob when it reaches the lowest position. (Take $g = 10 \ m/s^2$) (in $m/s$)

Two pendulums of length $121 \ cm$ and $100 \ cm$ start vibrating in phase. At some instant,the two are at their mean position in the same phase. The minimum number of vibrations of the shorter pendulum after which the two are again in phase at the mean position is:

The periodic time of a simple pendulum of length $1\, m$ and amplitude $2\, cm$ is $5\, s$. If the amplitude is made $4\, cm$,its periodic time in seconds will be