# Thought Prob : Regenerative Damping of a Simple Harmonic Oscillator

• Hepth
In summary, the conversation discusses different methods of converting the energy from a simple harmonic oscillator into an electrical current. The two methods mentioned are using a piezoelectric crystal or a magnetic coil, and the potential applications and limitations of each method are also discussed. There is also a suggestion to use a rack and pinion gear to run a standard generator, and a consideration of how to maximize energy extraction from the system.
Hepth
Gold Member
So I was just thinking about regenerative braking, piezoelectric sensors/strain gauges, magnetic-induced currents etc. and I thought of a question that would make a simple/decent discussion/practice in general engineer/physics (lots of /'s)

Suppose you have a simple harmonic oscillator :: WALL :: SPRING :: MASS

And assume its initial state is variational (Xo,Vo can be anything).

Now let's decide that we want to grab all of the energy out of the mass (as much as possible) and convert it to an electrical current.

I can think of two ways to do this:

1. The wall is a piezoelectric crystal. Set the Sqrt[k/m] to the natural freq of the crystal to maximize efficiency.

2. Magnetic fixed MASS, entire thing is inside a coil.

Can anyone think of any other ways of doing this? Of these two I think each has its application depending on the scale of the SHO. Both can be optimized for whatever the actual application, but I was trying to think of other methods.

I feel like they've done something similar somewhere (maybe using floatation devices to harvest energy from waves?) Though I was thinking on a smaller scale than that but it doesn't matter, I'm more interested in discussing general engineering applications to this.

It almost comes down to converting 1-D linear mechanical motion to an electric current. So assume no rotation is available (otherwise coiled motor/generator would be the solution). Thinking about 2: If there was a fluid inside the cavity that was ferromagnetic but with low viscosity, could the resistance of the fluid be overcome by the increasing of the electromagnetic permeability?

Thanks! Just thought I'd put this out there and see if anyone had any good ideas.

-Hepth

Why don't you try a rack and pinion gear, and run a standard generator on the pinion gear.

Issue with method 1 is that you'd have to have an incredibly small mass on a pretty high-stiffness spring.

Issue with method 2 is that the current would be AC, but I think this would be the best method.

Also, you might get more total energy out of the system by absorbing *all* of the spring energy during a single period (complete damping), since energy is lost as heat while the spring itself is deforming. This provides some considerable energy loss, more than you would through keeping something spinning with, say, a bearing. You want to suck as much energy as you can from the spring-and-mass system as quickly as possible to avoid this type of loss; a pendulum given the same amount of energy will stay in motion much longer than a mass on a spring, unless we're comparing a crappy pendulum to an incredibly thin/long spring.

Consider applying Bob S's idea to run a rack and pinion assembly where the pinion (circular gear) is relatively heavy and thus slow to spin up, and have the rack sufficiently short so that it slides off the pinion right as the spring reaches its unstrained/neutral midpoint (x=0). Because the rack will only be slowly spinning the pinion, once it uncouples it will not have nearly any momentum remaining, so nearly as much energy will have been extracted from the system as possible.

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## 1. What is regenerative damping?

Regenerative damping is a process where the energy lost in a system due to damping is regained and used to sustain the motion of the system.

## 2. How does regenerative damping affect a simple harmonic oscillator?

In a simple harmonic oscillator, regenerative damping can increase the amplitude of the oscillations and reduce the time taken for the system to reach its steady state.

## 3. What are the benefits of regenerative damping in a simple harmonic oscillator?

The main benefit of regenerative damping in a simple harmonic oscillator is that it can help maintain the oscillations without the need for an external energy source. This can be useful in situations where a continuous and sustained motion is required.

## 4. What factors influence the regenerative damping of a simple harmonic oscillator?

The regenerative damping of a simple harmonic oscillator can be influenced by factors such as the stiffness of the system, the damping coefficient, and the frequency of the oscillations.

## 5. How is regenerative damping calculated in a simple harmonic oscillator?

The calculation of regenerative damping in a simple harmonic oscillator involves determining the amount of energy lost due to damping and the amount of energy regained through regenerative damping. This can be done using mathematical equations and the specific parameters of the system.

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