1. The problem statement, all variables and given/known data The potential energy of a particle of mass m near the position of equilibrium is given by U=U0sin2(αx) where U0 and α are constants. Find the frequency of the small oscillations about the position of equilibrium. 2. Relevant equations Work energy equation (1/2)kx12+(1/2)mv12=(1/2)kx22+(1/2)mv22 3. The attempt at a solution (1/2)kx2=U0sin2(αx) Differentiating twice and rearranging: k=2U0α2cos(2αx) I'm confused from here. Am I supposed to use the work energy relation? I vaguely remember learning about sin(θ)≈θ when θ is small and also about Taylor expansion. Any hints will be appreciated.