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X = Magnitude*Exp(-time/decay_rate)*sin(2pi*frequency*time + PhaseShift*time)

What is normally done using mechanical pendulums can also be done on a spread sheet. If the spread sheet also provides the slider function, this can provide much greater controls over the various pendulum parameters.

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The spreadsheet in OpenOffice does provide a working slider control which can set the value of a given cell.

In this case the X values has frequency, magnitude, decay, and phase parameters which follows this equation.

X = Magnitude*Exp(-time/decay_rate)*sin(2pi*frequency*time + PhaseShift*time)

X = Magnitude*Exp(-time/decay_rate)*sin(2pi*frequency*time + PhaseShift*time)

Both the OpenOffice and Excel version are included. The Excel version unfortunately appears to have problems getting its slider controls to work properly, at least on a MacBookPro. If you download the Openoffice version, the file's extension my need to be changed to something like "FWVEAA8FR123iEH.ods".

Pendulum_Art.ods143 KB

pendulum_art.xls81 KB

Light_Lab3 years agoReply

I built a real pendulum harmonogram when I was a kid and I tried many years ago to do the patterns in Excel. I could never get enough data sets in Excel though to make smooth lines. Nowadays In the lab we are always running out of data space with Excel so we use Origin.---- You have used a nice trick via the smooth lines function so you don't need as much data. The only problem is the curves are NQR when you get into some patterns. I one day I might try this in Origin.

dsauer (author) 3 years agoReply

You might want to check out an open source program called SCILAB. I have a cheat sheet on how to use it here. http://www.idea2ic.com/PlayWithFink/scilab_Picture/SCILAB%20Templates.html This cheat sheet includes 25 lines of cut and paste text that will do a 3D plot. So the harmonogram can be done in 3D. I have long list of things I plan to do in 3D.

Light_Lab 3 years agoReply

Thanks for the lead seems like SCILAB is similar to MatLAB which I can get a company license for but takes some money from my budget. Looks like SCILAB is free I will definitely follow that up. Yes 3D harmonograms would be cool but don't over look the fact that you can mathematically model the vector sum of any number of pendulums in 2D or 3D; and use other functions than simple sines. Many things you cannot do with a mechanical harmonogram. BTW I once tried putting a loosely strung rubber band on one of the pendulums made a cool variation.

dsauer (author) 3 years agoReply

The mechanical harmonogram looks like it would be fun to build. Its just that the internet puts us all in touch with a lot of fun things to do. Not enough time to do them all. But it is fun to see someone else doing them as an instructable.

spiderfurby4 years agoReply

very clever - do you have more examples?

dsauer (author) 4 years agoReply

For some reason I can't cut and paste here. My email is dsauersanjose@aol.com. I can always send you an email.

Light_Lab 3 years agoReply

Paste into Windows Paint (under accessories); save as a BMP and then just use the Instructables image manager. Then you can add them to your article or emails.

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