Wolfram Demonstrations Project: "A Non-Harmonic Oscillator"

To use this demonstration, you must download and install the Mathematica Viewer from the Wolfram Demonstrations Project. This demonstration illustrates a very simple example of a non-harmonic oscillator - a helium balloon on a string. There are two sources of non-linearity. First, as the balloon rises, it lifts more string. Therefore, the mass of the oscillator is a function of the position of the oscillating mass, which leads to nonlinear behavior. In addition, a damping term has been included which mimics the effect of air resistance. Adjust the various control parameters to gain a feel for which parameters have a larger effect of the motion of the oscillator. Check out the special cases suggested in “Details” section of the demonstration: motion in the absence of damping (set the damping constant to 0), motion of the balloon when the string has no mass – then, the force of gravity no longer increases as the balloon goes up, and the motion when mass of the string is large and the damping constant is large – what happens to the balloon eventually in this case?