A simple pendulum of length is suspended from the ceiling of a car moving with a speed u on a circular horizontal road of radius r. (a) Find the tension in the string when it is at rest with respect to the car. (b) Find the time period of small oscillation.

(a) ma

(b) where


(a)when pendulum is in rest with respect to car, the free body diagram will be as follows

The tension in the string will be due to force due to gravity and

Force due to centripetal force

Here is the acceleration on the bob

(b) Time period of the small oscillation

From previous problem, we know