It is given that a bob with a string is hanging in a car that is travelling with a constant speed v around a circle of radius R. The required centripetal force is obtained by the incline of the string attached to the bob by angle from the vertical. The component of the weight of the bob perpendicular to the string provides the centripetal force, that is

Let the bob be displaced by a small angle . We will show that for small oscillation the bob will execute simple harmonic motion as a simple pendulum.

When the pendulum is displaced by an additional angle restoring force on the bob will be

Let us consider motion in a uniformly rotating frame with angular speed . Let the length of the string with which the bob is hanging be L. Equation of motion of the bob in this frame of reference will be

Under the approximation

,

equation of motion reduces to the form

Using the result

equation of motion simplifies to the form

It is an equation of SHM. Frequency of oscillation is

where T is the period of oscillation. Frequency of the pendulum is