I am currently studying mechanical engineering and as a part of the course we have an assigenment to solve a problem with an inverted pendulum. After a while we ended up with a differential equation that we have no idea on how to solve, do you have any tips? Would it be possible to find a function for $\varphi(t)$ that fulfills the constraint?
Thanks.
$L=\frac{I+M(L+r)^2}{M(L+r)}$
assume $\lvert\varphi(t)\rvert \ll 1$
$$\varphi''(t) = \frac{-(R\Omega^2\sin(\Omega t)-g)\varphi(t)+R\Omega^2\cos(\Omega t)}{L}$$