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


a 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


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