Showing SHM

1. The problem statement, all variables and given/known data

A cube of mass m is connected to two rubber bands of length L, each under tension T. The cube is displaced by a small distance y perpendicular to the length of the rubber bands. Assume the tension doesn’t change. Show that the system exhibits SHM, and find its angular freqency ω.

3. The attempt at a solution

So basically from a FBD of cube, I have vertical forces: -2Tsinθ – mg = m$\frac{d^2y}{dt^2}$ and the horizontal components of tension from each band cancels. Now since the cube is displaced by a small distance y, I assume we can approximate sinθ ≈ θ. But then I’m not sure what to do?
I tried using sinθ = $\frac{y}{(y^2+L^2)^{1/2}}$, but then I get a complicated expression.
I know I need to obtain a -constant*y on the LHS. Any suggestions.

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