You should end up with a differential equation that is of the form:
This integral cannot be solved in terms of a closed-form expression.
It can be transformed into an Elliptic Integral which could, in principle,
be inverted to solve for theta(t). In practice, the differential equation
could be solved numerically. When g = 9.81 m/s^2 and a = 0.0981 m, the graph
of theta(t) looks like this: