The length of a simple pendulum is increased by $1\%$. Its time period will

If the mass of the bob in a simple pendulum is increased to thrice its original mass and its length is made half its original length,then the new time period of oscillation is $\frac{x}{2}$ times its original time period. Then the value of $x$ is

Two simple pendulums of lengths $1.44 \, m$ and $1 \, m$ start swinging together. After how many vibrations will they again start swinging together?

The period of oscillation of a simple pendulum of length $L$ suspended from the roof of a vehicle which moves without friction down an inclined plane of inclination $\alpha$,is given by

The time period of a simple pendulum inside a stationary lift is $\sqrt{3} \ s$. When the lift moves upwards with an acceleration $g/3$,the new time period will be ($g=$ acceleration due to gravity).

$A$ person of mass $M$ is sitting on a swing of length $L$ and swinging with an angular amplitude $\theta_0$. If the person stands up when the swing passes through its lowest point,the work done by him,assuming that his centre of mass moves by a distance $l$ $(l << L)$,is close to