A rigid rod of length L, supported at one end by a frictionless hinge, connected to an electric motor, through which rapid vibrations are forced hinge in the vertical direction:
$$S = A\sin(\omega t)$$
Applying Newton's second law gives the equation of motion:
$$\theta'' = \frac{3}{2L} (g - A \omega^2 \sin(\omega t))\sin(\theta)$$
I need to consider the following options and interpret them physically:
The values P, Q, R are given. For the first two options, the duration of the process T=1.8 sec. For other options T=0.5 sec.
So, I have no idea how to solve this differential equation at all. Also, I should solve it using Runge–Kutta–Fehlberg method. It seems like I should use reduction of a high-order differential equation to system of equations of the first order, but I don't sure.