NEETSHMHard
Question
The potential energy of a particle of mass ′m′ situated in a unidimensional potential field varies as U(x) = U0 [1 − cos ax], where U0 and a are constants. The time period of small oscillations of the particle about the mean position −
Options
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Solution
Restoring force F = 
(u0 (1-cos ax)
F(x) = − u0 a sin ax
for small angle sin ax ≈ ax
F = − u0a2x ⇒ acc =
= −ω2x = 
× x
So, Time period T = 2π
(u0 (1-cos ax)F(x) = − u0 a sin ax
for small angle sin ax ≈ ax
F = − u0a2x ⇒ acc =
= −ω2x = × xSo, Time period T = 2π
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