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Malcolm's ruler machine
Hi All,
I have built sort of a fun toy to study secondary resonance. Going off
Malcolm's analogy of a bent ruler model for secondary oscillation, I built
a simple device.
http://users.better-dot-org/tfritz/site/misc/MalRulMa/Mach.jpg
It is simply a wooden base with a spring steel wire pressed into a hole. A
"woofer" speaker is connected to the base of the wire by a rubber band and
some small powerful magnets to couple the speaker cone to the base of the
wire. The wire is 30.0 inches long and weighs 11.7 grams. The wires
natural frequency is 1.81 Hz.
The speaker is driven by a DC-50kHz amplifier from a low frequency
oscillator with a scope attached to measure frequency:
http://users.better-dot-org/tfritz/site/misc/MalRulMa/drive.jpg
The first harmonic occurs at 1.81Hz where the wire swings with great
amplitude. Decreasing the amplitude did not change the resonant frequency:
http://users.better-dot-org/tfritz/site/misc/MalRulMa/1st.jpg
The third harmonic occurs at 12.11Hz with far less amplitude. The nodal
point is 23.5 inches from the base:
http://users.better-dot-org/tfritz/site/misc/MalRulMa/3rd.jpg
The fifth harmonic is at 34.13Hz with nodes at 15.25 and 26.0 inches:
http://users.better-dot-org/tfritz/site/misc/MalRulMa/5th.jpg
The seventh harmonic is at 66.23 Hz with nodes at 10.75, 19.25, 27.0
http://users.better-dot-org/tfritz/site/misc/MalRulMa/7th.jpg
it is interesting to compare this to actual secondary coil measurements at:
http://users.better-dot-org/tfritz/VoltDistBare.jpg
Is is also interesting to note the similarity of the wire bending profile
to the graph profile of the measured results:
http://users.better-dot-org/tfritz/site/misc/MalRulMa/Wire.jpg
It is interesting to also note the measured profile is concave rather than
convex as would be expected in a 1/4 wave sine function as shown in the
comparison graph here:
http://users.better-dot-org/tfritz/DistGraph.jpg
I don't know what all this means or anything but I wanted to pass this
information I had on for everyone's enjoyment... Maybe it will all mean
something to someone. I have been so busy getting the thing working that I
have not thought much about the implications...
For reference, there are many web sites with spring, mass, and oscillation
information such as:
http://www.futuresouth-dot-com/~mhenders/physics/Simple_Harmonic_Motion.htm
http://www.cs.wright.edu/~fdgarber/199/Spring_Mass_3/
I will try adding weight at the top (like a terminal load) and such in the
future. I have to start working on the cap bulk buy first ;-))
Cheers,
Terry