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
A.
B.
C.
D.
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
Create a free account to view solution
View Solution FreeMore SHM Questions
The composition of two simple harmonic motions of equal periods at right angle to each other and with a phase difference...A particle is describing SHM with amplitude ′a′. When the potential energy of particle is one fourth of the ...The maximum time period of oscillation of a simple pendulum of large length is:...A child swing on a swing in sitting position, stand up, then the time period of the swing will...A string OP of length L is fixed at both ends and vibrates in its first overtone with time period T and maximum amplitud...