Forced Damped Vibration

This applet shows the solution of a forced damped spring-mass system: $\dsy'' + \gamma y' + y = F_0 \cos(\omega t)$,$$\,y(0) = y_0$$, $\,y'(0) = y'_0$, for $0 \le t \le 65$.

You can adjust the damping constant $\gamma$, forcing angular frequency $\omega$, forcing amplitude $$F_0$$ and initial conditions $\,\!y_0$ and $\,\!y'_0$ by using the sliders, or typing a value in the box at the right and pressing Enter. The allowed ranges of these parameters are as follows: $0 \le \gamma \le 4$, $0 \le \omega \le 3$, $0 \le F_0 \le 5$,$-10 \le y_0 \le 10$, $-10 \le y'_0 \le 10$.

The forcing term $F_0 \cos(\omega t)$ is shown in green, and the solution y in red. If you click on the graph, the coordinates [t,y] of the point where you clicked are shown at the top left of the graph.