Computed Pendulum Waves

Pendulum waves computed using the differential equation d^2(theta)/dt^2 = - omega^2 * sin(theta) - gamma * sgn[d(theta)/dt] * [L * d(theta)/dt]^2. All the pendulums started at a distance of 0.231 m from their equilibrium point and gamma was set to 0.05. The small amplitude periods of the pendulums were chosen so that after 60 seconds the number of cycles for each pendulum varied from 32 to 44 exactly in steps of one cycle. The frame rate is 60 per second.

The nonlinearity alters the period of the oscilations depending on the amplitudes. With weak dampening the amplitudes do not change much and the amount of dampening per cycle does not change much over relatively short periods of time but a Stokes dampening term proportional to - d(theta)/dt would probably be more accurate, theoretically, for lower speeds.

string length formula: L(k) = 894 meters / k^2

Category:

Science & Technology

Tags:

• computed
• nonlinear
• pendulum
• waves

[AeroJimE27]

What program did you use?

[httprover]

@AeroJimE27 I used Mathcad 11 to plot single frames along with some "see through" data then used its animation tool to capture the video.

[pintodaguanatoioba]

hello I am doing a school project and the teacher gave this challenge (to build the pendulum), but my friends and I did so that the balls were all uncoordinated, could you put the wires and measure the frame size, to help me pendulum do?

and also the weight of the marbles, all have the same weight?

[TupoyVolk]

Thanks for the description. Interesting that you included Rayleigh drag.

[LawrenceBall]

These are primitive example of the late John Whitney's Differential Dynamics which he used in his computer films. With the help of Mike Tusch and Dave Snowdon over 15 years, I have developed techniques on the shoulders of Whitney's principle which we call harmonic maths. I used HM for Pete Townshend's Lifehouse-Method musical portraiture system. With graphics speeds today, we can choreograph 30,000 points calculated in realtime. see lawrenceball org and visualharmony org