This shows the motion of a driven damped harmonic oscillator, described in terms of the undamped natural frequency, and a frequency gamma that reflects the degree of damping, parameterized as a damping ratio gamma/natural frequency.
The oscillator is driven with a force that is a sine function of time, with a frequency that can be varied, expressed as a forcing ratio driving frequency/natural frequency.
An accurate solution requires a small time step and RK4 as the integration algorithm.