Consider a pendulum oscillation problem, where pendulum oscillates around the vertical in the downward configuration.
Assume that there is no friction at the pivot point around which the pendulum rotates, and assume that there exists a torsional spring that counter acts the pendulum motion. Let the spring force Fs be a non-linear function of the displacement of the pendulum θ from the vertical configuration, that is,
Considering the presence of gravitational forces, ignoring external torques on the pendulum
To find a the differential equation governing the pendulum dynamics.
The Attempt at a Solution
I am tying to find T as a function of F