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 Homework Statement
 A particle of mass ##m## is located in a unidimensional potential field where the potential energy of the particle depends con the coordinate ##x## as ##U(x)=U_0(1\cos ax)##; ##U_0## and ##a## are constants. Find the period of small oscilations that the particle performs about the equilibrium position.
 Homework Equations

##x''+\omega^{2}x+0##
##T=2\pi /\omega##
I first found the equilibrium points taking the derivative of the potential. ##U'(x)=U_0 a\sin(ax)##, and the equilibrum is when the derivative is 0, so ##U_0 a\sin(ax)=0## so ##x=0## or ##x=\pi/a##. Taking the second derivative ##U''(x)=U_0a^2 \cos(ax)## I find that ##x=0## is a minimum point, since the second derivative is greater than 0, and ##x=\pi/a## is a maximum point. But if I replace any of those points on the first derivtive, I get 0. I don't know what to do.