When you have the torsion spring connected to the pendulum, you don't have any sort of simple equation you can use any more ... you have to just add the torques up.
First, you have a torque due to the weight of the hanging deal, something like (weight)(radial distance)(sin of inclination angle) if you're not into vectors. That pulls the thing back to equilibrium.
The torsion spring provides a little 'kick' in the opposite direction to keep it going. The torque provided is just proportional to the angle, (kappa)(theta)
In total you have then (weight)(radial distance)(sin theta) - (kappa)(theta) = net torque. The net torque must be the moment of inertia times alpha, the second derivative of angle with respect to time. If you use the low-angle approximation sin(theta)~theta, you can recover an equation for simple harmonic motion: angular acceleration is (omega)^2 times angle.
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