Question

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?

Answer 1

See the figure ,
ar = v²/R
where ar is radial acceleration
V is speed of car on circular track .
R is the radius of circular track .

Hence, effective acceleration vector = -v²/R i -gj
Magnitude of effective acceleration = √( g² + v⁴/R²)

We know,
T = 2π√(L/aeff)
= 2π√{L/√(g² + v⁴/R²)}
= 2π√{L/(g² + v⁴/R²)}