All Problems

Mechanical Oscillations

Problem 4.16

A particle of mass mm is located in a unidimensional potential field where the potential energy of the particle depends on the coordinate xx as U(x)=U0(1cosax);U0U(x)=U_{0}(1-\cos a x) ; U_{0} and aa are constants. Find the period of small oscillations that the particle performs about the equilibrium position.

Reveal Answer
T=2πm/a2U0T=2 \pi \sqrt{m / a^{2} U_{0}}