1. The problem statement, all variables and given/known data A particle of mass m is on a massless string of length 3a, which is held horizontally across with a tension T(which you can assume doesn't change with the small vibrations). The particle is a distance of a from one of the edges. Set up a diff. equation that describes the particles motion with time and find its frequency of oscillations. 2. Relevant equations mx'' = net force x''+(ω^2)x=0 => x=Acos(ωt+φ) 3. The attempt at a solution I originally wrote mx'' = T - mg but this doesn't work since it doesn't involve x and doesn't account for the changing sign of T depending if that particle is above or below the equilibrium point. I tried to describe its position but the best I could do was x(θ) = arctan(x/a) and not x(t) which is what I want (at least I think because then I could take the derivative twice and get the acceleration). Any tips would be appreciated!