SHMEasy
Question
The potential energy of a particle of mass 1 kg in motion along the x-axis is given by :
U = 4(1 - cos2x)J, where x is in metres. The period of small oscillations (in sec) is :-
U = 4(1 - cos2x)J, where x is in metres. The period of small oscillations (in sec) is :-
Options
A.2π
B.π
C.π/2
D.√2π
Solution
F = 
= - 8sin 2x
a =
= -8sin 2x (∵ m = 1kg)
For small oscillations, sin2x = 2x
i.e., a = - 16x
Since a ∝ - x
The oscillations are SH in nature.
∴ T = 2π
sec
= - 8sin 2xa =
= -8sin 2x (∵ m = 1kg)For small oscillations, sin2x = 2x
i.e., a = - 16x
Since a ∝ - x
The oscillations are SH in nature.
∴ T = 2π
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