Non-Sinusoidal Oscillation: A Balloon on a String

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Picture a buoyant balloon trailing a string with some mass per unit length. As the balloon rises, more string is lifted off the floor and the weight of the balloon-string system increases. As the balloon sinks, string returns to the floor and the weight of the balloon-string system decreases. In effect, the mass of the system depends on its position.

Contributed by: Dillon Tracy (March 2008)
Based on a program by: Mark Robertson-Tessi
Open content licensed under CC BY-NC-SA


Snapshots


Details

Snapshot 1: no damping; the displacement curve (blue) might look like a simple harmonic oscillator at first glance, but look at its derivatives and ; note that energy is not conserved even in the absence of damping, as the rope is making inelastic collisions with the floor

Snapshot 2: massless string (and no damping); up, up, and away: in this case, the balloon is under the constant acceleration of its own lift

Snapshot 3: heavy string, small balloon, significant damping; the balloon reaches equilibrium around



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