Question

A simple pendulum of length l with 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?

Answer 1

The bob of the simple pendulum will experience acceleration due to gravity and the centripetal acceleration provided by the circular motion of the car.

Acceleration due to gravity = g

Centripetal acceleration =$\frac{v^2}{R}$

Where,

v is the uniform speed of the car

R is the radius of the track

Effective acceleration (aeff) is given as:

$a_{eff}=\sqrt {g^2+(\frac{v^2}{R})^2}$
Time period, $T=T=2π\sqrt \frac{l}{a_{eff}}$

Where, l is the length of the pendulum

∴ Time period, $T = 2π\sqrt{\frac{l}{g^2+\frac{v^4}{R^2}}}$