Damped Vibrations -- Help
The graphing window at top right displays a solution of the differential
equation mx" + bx' + kx = 0 .
A yellow diamond in the left window represents the initial condition in the (x',x) phase plane. The trajectory of (x',x) in the phase plane is also displayed (limited to ten loops of the spiral ahead and behind t = 0 in the underdamped case). The yellow diamond moves along the trajectory when time is varied.
The initial condition is set by dragging the yellow diamond or the sliders at bottom and left side of the phase plane window.
The [Relate diagrams] key toggles a faint yellow line connecting the point
on the (x',x) plane with the corresponding point on the graph. A slider below
this key controls a zoom feature in x and x' and the maximal displayed values
Sliders at lower left control values of m, b, and k.
The [Roots] key toggles a display of the roots of the characteristic polynomial p(s) = ms2 + bs + k , and their values are read out at lower right, in green if non-real, blue if real and distinct, and red if repeated.
© 2008 H. Hohn, H. Miller and J.-M. Claus