Answer:
Given parameters:
A particle of mass m is located in a one-dimensional potential field and
Potential energy (P.E) = V(x)=A(1−cos px)
The force experienced by the particle of mass m is
F = – (dV/dx)
F = – ( d(A(1−cos px)/ dx)
F = – Apsinpx
For small oscillations
F = ≈−Ap2x
Acceleration (α) = F/m
α = – (Ap2/m)x
But α = F/m
α = -ω2x
So ω = √Ap2/m
The period of small oscillations of the particle (T) = 2π/ω
T = 2π/(√Ap2/m)
T = 2π√m/Ap2