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For pedagogic reasons I am looking for applications in engineering for the simple spring harmonic oscillator, i.e. something like this ("harmonic" implies in particular "without damping"): enter image description here.

The angle to the horizontal my be between 0 and 90 degree and one spring may be missing.

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  • $\begingroup$ I know you said without damping, but I was told about a metal chimney in high winds that was vibrating due to wind shedding and they attached steel cables to it with the other ends fixed to large concrete blocks (>500Kg) which were on a slope : these then caused a change in the chimney's natural frequency - which stopped it failing. $\endgroup$ – Solar Mike Sep 5 '17 at 21:20
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    $\begingroup$ I think you are going to have a hard time finding any applications that don't consider damping. The reason is because "damping" is basically the same thing as "energy transfer to somewhere else" which is what happens if the device actually has some functional behaviour. With no damping, you can put some energy into the device to make it oscillate and it will continue oscillating "for ever" - and that's pretty much all it can do, which isn't very useful in any practical situation I can think of. $\endgroup$ – alephzero Sep 5 '17 at 23:14
  • $\begingroup$ You might be able to come up with some examples based on steady state forced response (but not at the system's resonant frequency) - for example vibration isolators. which allow the system to "self center" its motion when running above the resonant frequency. But you will have to ignore (or tell "lies-to-children" about) how the system can get into such a state, with no damping to eliminate the startup transient motion, and how you accelerate through the resonance without breaking anything! $\endgroup$ – alephzero Sep 5 '17 at 23:22
  • $\begingroup$ spring oscillators are (or were) used as the timing mechanism in clocks. Typically spiral coil springs, not linear as you have pictured. $\endgroup$ – agentp Sep 6 '17 at 15:51
  • $\begingroup$ @agentp but they were damped oscillators, otherwise the amplitude of oscillation would have increased indefinitely. Sure, the damping was very low, but the clock would not have worked without it! Even the "tick tock" noise is radiating sound energy, which is damping the oscillations! $\endgroup$ – alephzero Sep 7 '17 at 2:48
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While nothing in the real world truly has zero damping, a good example, though it doesn't use a coil spring would be a tuned mass vibration absorber.

"Tuned Dynamic Vibration Absorber"

It's basically a mass attached to a motor, or another vibrating object by a stiff rod. By varying the amount of mass and the stiffness of the rod, the absorber can be "tuned" to have a natural frequency matching the dominant frequency of the motor's vibration. (For most electric motors driven with 60Hz AC, this will be 120Hz)

When the motor runs, the 120Hz vibration of the motor will drive the absorber at resonance instead of driving the attached structure which would create noise.

While these absorbers are similar in concept to the "Tuned Mass Dampers" seen in large buildings, a tuned mass absorber does not require damping to function.

Here's a nice explanation from Penn State

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You could compare spar buoys to discus buoys in terms of spring constant of equivalent models, and introduce the idea of driver response as well.

Pedagogically speaking, oscillating systems are part of the engineering environment. We need to recognize, accommodate, and sometimes mitigate their effects more so than design and construct them. Harmonic oscillation is an analysis tool, not a design tool.

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