Which of the following plots represents schematically the dependence of the time period of a pendulum,if measured and plotted as a function of the amplitude of its oscillations? (Note: amplitude need not be small)

If the length of an oscillating simple pendulum is made $\frac{1}{3}$ times at a place while keeping the amplitude the same,then its total energy $(E)$ will be: (in $E$)

Choose the correct length $(L)$ versus square of time period $(T^2)$ graph for a simple pendulum executing simple harmonic motion.

$A$ small sphere of radius $r$ is placed on a concave surface of radius of curvature $R$ a little away from the center. When the sphere is released, it oscillates. Assuming the oscillation to be simple harmonic motion and $r << R$, then the time period is

$A$ 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 $10 \ m/s^2$?

$A$ mass falls from a height $h$ and its time of fall $t$ is recorded in terms of time period $T$ of a simple pendulum. On the surface of the Earth,it is found that $t = 2T$. The entire setup is taken to the surface of another planet whose mass is half that of the Earth and radius is the same. The same experiment is repeated and corresponding times are noted as $t'$ and $T'$.