A simple pendulum of initial length \(l_{0}\) and initial angle \(\theta_{0}\) is released from rest. If the length is a function of time according to \(l=l_{0}+\varepsilon t\), find the position \((l, \theta)\) of the pendulum at any time assuming small oscillations. The governing equation of motion will turn out to be

\[ \left(l_{0}+\varepsilon t\right) \ddot{\theta}+2 \varepsilon \dot{\theta}+g \theta=0 \]

and in transformed Bessel form, \[ x^{2} \theta^{\prime \prime}+2 x \theta^{\prime}+\frac{x g}{\varepsilon^{2}} \theta=0 \]
where \(x=l_{0}+\varepsilon t\). (This problem requires the use of Bessel functions.)