A simple pendulum of length L and mass m is suspended in a car that is traveling with a constant speed v around a circle of radius R. If the pendulum endergoes small oscillations in a radial direction about its equilibrium position, what will its frequency of oscillation be?

(a)
The period T of a simple pendulum is defined as,
T = 2π√L/g
Here L is the length of the pendulum and g is the free fall acceleration.
So, the period of the simple pendulum is independent of the mass m of the suspended particle.
Thus the mass, m, of the cord attached to the bob, of mass M, of a pendulum will not affect the period over that for a simple pendulum in which m=0.
(b)
In a simple pendulum, the period T will be,
T = 2π√L/g
Here L is the length of the pendulum and g is the free fall acceleration.
The period of the simple pendulum is independent of the mass m of the suspended particle.
A simple pendulum is an idealized body consisting of a particle having mass M, suspended by a light inextensible cord. When pulled to one side of its equilibrium position and released, the pendulum swings in a vertical plane under the influence of gravity. The motion is periodic and oscillatory. As here, a cord of length L swinging without anything on the end (M=0), therefore, it will not an ideal simple pendulum anymore. Because, an ideal pendulum always contain a particle having mass M suspended by a light inextensible cord.