I want to solve the below equation to get find a general solution for $\theta(t)$. Is the next step acceptable or do I have to take into account $\dot{L}$ as well ? $$ \ddot{\theta} = -2 \frac{\dot{L}}{L}\dot{\theta} $$ Applying laplace transform,
$$ s^2\phi(s)-s\theta(0) - \ddot{\theta}(0) = -2 \frac{\dot{L}}{L}[s \phi(s) - \theta(0)] $$