Answer the following questions:

What is the frequency of oscillation of a simple pendulum mounted in a cabin that is freely falling under gravity?

Answer the following questions:

The motion of a simple pendulum is approximately simple harmonic for small angle oscillations. For larger angles of oscillation, a more involved analysis shows that T is greater than . Think of a qualitative argument to appreciate this result.

Answer the following questions:

A man with a wristwatch on his hand falls from the top of a tower. Does the watch give correct time during the free fall?

A simple pendulum of length l and having a bob of mass M is suspended in a car.

The car is moving on a circular track of radius R with a uniform speed v. If the pendulum makes small oscillations in a radial direction about its equilibrium position, what will be its time period?

A cylindrical piece of cork of density ρ of base area A and height h floats in a liquid of density ρ_l. The cork is depressed slightly and then released. Show that the cork oscillates up and down simple harmonically with a period

Where ρ is the density of cork. (Ignore damping due to viscosity of the liquid).