Linear oscillator

This simulation solves the harmonic oscillator with or without linear damping and external sinusoidal force:
x'' + 2 γ x' + ω²x = f cos (Ω t + δ)
where each ' denotes a time derivative.

You can select below the parameters γ, f, Ω and δ, as well as the initial conditions for the elongation x and the velocity v = x' (x and v can also be selected by moving with the mouse the point on the display Phase space).
The unit time is 1/ ω (so that ω = 1).
For information on other elements, put over them the mouse pointer to get a tooltip.
It is possible to draw the x(t) evolution, the phase space (x,v) and the evolution of the mechanical energy (when f = 0, one gets with the latter the graph of the potential energy in red).

Activities

Set γ = 0 and f = 0 and solve the system for different initial conditions to see linear periodic oscillations.
Select Energy to see the potential energy V(x) = 1/2 x² in red and the mechanical energy E = 1/2 x'² + V(x) in blue.
Set γ = 0.05 and f = 0. What happens now with the mechanical energy for different initial conditions?
Set γ = 0.1 and f = 0.1. What would happen with the equilibrium point?
After a while (say t = 100), click Erase to clear all graphs. How is the remaining (nearly asymptotic) motion?
What changes if you choose other initial conditions?
Select for Ω a value near resonance, say 1 or 0.995. What would happen?
What happens with smaller values of γ?

This is an English translation of the Basque original for a course on mechanics, oscillations and waves.
It requires Java 1.5 or newer and was created by Juan M. Aguirregabiria with Easy Java Simulations (Ejs) by Francisco Esquembre. I thank Wolfgang Christian and Francisco Esquembre for their help.