MBK UNFORCED

This applet explores the differential equation modeling an unforced spring-mass-damper system. The differential equation is \[mx'' + bx' + kx = 0\]

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

The initial conditions are can be set with the x0 and x1 sliders. We have \(x(0) = x0\) and \(x'(0) = x1\)

The time \(t\) can be changed by sliding the small vertical line on the \(t\) axis of the time graphing window (left hand window). The values of time and \(x(t)\) are displayed below the graphing window.

The 'Show roots' checkbox determines if the roots (also known as poles) are shown numerically and graphically. This window also shows the root locus, which is the curve the roots lie on when \(m\) and \(k\) are held fixed and \(b\) changes.

The time graphing window can be zoomed in both directions using the t-zoom and x-zoom sliders. It can also be shifted left or right by holding the mouse down and dragging inside the graph window.

If your mouse is in either graphing window the coordinates of the mouse position are displayed above the graph.