MBK Prime

This applet explores the differential equation modeling a spring-mass-damper system. The differential equation is \[mx'' + bx' + kx = \cos(\omega t)'\]

In each of these models we consider the function \(\cos(\omega t)\) to be the input to the system. Both the input and periodic response are plotted in the large graph on the left. The linear gain is plotted in the graph on the upper right. (Since the input has amplitude 1, the gain is the same as the output amplitude.) The phase lag is plotted in the graph on the lower right.

All of the parameters \(m, \, b,\, k, \, \omega\) are settable using their respective sliders.

The input frequency \(\omega\) can be changed by sliding the small 'knob' on the \(\omega\) axis of either the gain or phase graphing windows (right hand windows). The value of \(\omega\) is displayed between the two graphs.

The values of gain and phase lag are displayed above their respective graph windows.

The time \(t\) can be changed by sliding the small 'knob' on the \(t\) axis of the time graphing window (left hand window). The values of time, the input \(f(t)\) and output \(x(t)\) are all displayed near this window.

For all graphs, if your mouse is in the graphing window the coordinates of the mouse position are displayed above the graph.