The length of a seconds pendulum is $1 \,m$ on the earth. If the mass and diameter of a planet are double that of the earth, then the length of the seconds pendulum on the planet will be: (in $\,m$)

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

The time period of a simple pendulum is $T$. The angular amplitude is $\beta$. How much time will the bob of the pendulum take to move from the equilibrium position $O$ to position $A$,where the string makes an angle $\alpha$ with the vertical?

In an engine,the piston undergoes vertical simple harmonic motion with an amplitude of $7\, cm$. $A$ washer rests on top of the piston and moves with it. The motor speed is slowly increased. The frequency of the piston at which the washer no longer stays in contact with the piston is close to ...... $Hz$.

$A$ pendulum suspended from the ceiling of a train oscillates with a time period $2 \ s$,when the train is accelerating at $10 \ m/s^2$. What will be its time period when the train retards at $10 \ m/s^2$?

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