SHMEasy
Question
A particle of mass m is in a one dimensional potential field and its potential energy is given by the following equation U(x) = Uo(1 - cos αx)where Uo and α are constants. The period of the particle for small oscillations near the equilibrium will be-
Options
A.
B.
C.
D.
Solution
U(x) = U0(1 - cosαx)
F = -
= - U0α[sin α] ≈ - U0α2x
Therefore mω2 = U0α2 ⇒ ω =
⇒ T =
F = -
= - U0α[sin α] ≈ - U0α2xTherefore mω2 = U0α2 ⇒ ω =
⇒ T =
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