Pendulum in accelerating traincar

[buttermellow7]

Homework Statement

A pendulum bob of mass m is suspended by massless thread of length l from the ceiling of a boxcar. The car undergoes constant acceleration a along a straight, level track. What, in the small angle approximation, is the oscillatory period tau of the pendulum?

Homework Equations

F_g=mg\sin\theta=mg\theta
F_a=ma\cos\theta=ma

The Attempt at a Solution

mg\theta+ma=ml\ddot{\theta}
\frac{g}{l} \theta+\frac{a}{l}=\ddot{\theta}

What's the quickest way to solve this differential equation?

 

[member 553083]

My first idea was to Fourier transform it, but I'm not sure if that would be the best approach. Any suggestions?