Two oscillating simple pendulums with time periods $T$ and $\frac{4T}{3}$ are in phase at a given time. They will be again in phase after an elapse of time (in $T$)

The time period of a simple pendulum will be doubled if we

$A$ cylindrical piece of cork of density $\rho$, base area $A$, and height $h$ floats in a liquid of density $\rho_{l}$. The cork is depressed slightly and then released. Show that the cork oscillates up and down simple harmonically with a period $T=2 \pi \sqrt{\frac{h \rho}{\rho_{l} g}}$. (Ignore damping due to viscosity of the liquid).

The bob of a simple pendulum executes simple harmonic motion in water with a period $t$,while the period of oscillation of the bob is ${t_0}$ in air. Neglecting the frictional force of water and given that the density of the bob is $(4/3) \times 1000 \ kg/m^3$. What relationship between $t$ and ${t_0}$ is true?

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 ...... $Hz$.

Identify the correct statement.