A small block oscillates back and forth on a smooth concave surface of radius R (figure 12-E17). Find the time period of small oscillation.

Given radius of the concave surface = R

Let mass of the block be ‘m’

Driving force F = mgsinθ

Therefore a= gsinθ

agθ →1 [for small angles sinθ ]

if x is the displacement of block from mean postion then sinθ =x/R

θ x/R [for small angles sinθ ]

substituting in eqn 1 a = gx/R →2

from SHM equation a = x →3

comparing 2 and 3 we get ω =

Time period T = = 2π

1