$A$ pendulum has a time period $T$. If it is taken to another planet having an acceleration due to gravity half that of the Earth and a mass $9$ times that of the Earth,then its time period on the other planet will be:

The time period of a simple pendulum is $T$. The time taken to complete $5/8$ oscillations starting from the mean position is $\frac{\alpha}{\beta} T$. The value of $\alpha$ is ..... .

$A$ pendulum has a length of $0.4 \ m$ and a maximum speed of $4 \ m/s$. When the string makes an angle of $30^{\circ}$ with the horizontal,its speed will be: $\left[\sin \frac{\pi}{6} = \cos \frac{\pi}{3} = 0.5 \text{ and } g = 10 \ m/s^{2}\right]$

$A$ simple pendulum oscillates freely between points $A$ and $B$. We now put a peg (nail) at the point $C$ as shown in the figure. As the pendulum moves from $A$ to the right,the string will bend at $C$ and the pendulum will go to its extreme point $D$. Ignoring friction,the point $D$

$A$ simple pendulum is attached to the roof of a lift. If the time period of oscillation when the lift is stationary is $T$,then the frequency of oscillation when the lift falls freely will be

$A$ simple pendulum is suspended in a car. The car starts moving on a horizontal road according to the equation $x = \frac{g}{2} \sqrt{3} t^2$. Find the time period of oscillation of the pendulum.