Comonality Of Priciple.

[steve_bank]

A response to a post on another thread.

In the 90s when I took a night class in modern physics it was a little anti-climactic. Some of the general principles I understood from elect cal theory.

Principles of resonance and complex impedance are a general form that appear in electric circuits, mechanics, and hea flow.

In QM a rectangular potential well at the parcel level is a resonator.


Electrical impedance is one form of a generalized impedance function. Complex impedance electrcal or mechanical arises when there is a phase shift between excitation and response.


An electro-mechanical audio speaker serves as a complex impedance match between the electrical output impedance of the audio amplifier and the mechanical impedance of the air.


Resonance is also a generalized function across QM, Newtonian mechanics, and electric circuits.


A resonant electrical RLC circuit has the same 2nd order differential equation as a mechanical spring-mass- dashpot system. Any system with a 2nd order or higher differential equation can have an exponential(complex) response under dynamic excitation. .


Capacitance is a generalized form that appears in electric circuits, mechanics, and heat flow.

Mechanical impedance - Wikipedia

en.wikipedia.org

Mechanical impedance is a measure of how much a structure resists motion when subjected to a harmonic force. It relates forces with velocities acting on a mechanical system. The mechanical impedance of a point on a structure is the ratio of the force applied at a point to the resulting velocity at that point.[1][2]

Mechanical impedance is the inverse of mechanical admittance or mobility. The mechanical impedance is a function of the frequency ω of the applied force and can vary greatly over frequency. At resonance frequencies, the mechanical impedance will be lower, meaning less force is needed to cause a structure to move at a given velocity. A simple example of this is pushing a child on a swing. For the greatest swing amplitude, the frequency of the pushes must be near the resonant frequency of the system.

Analogues in mechanical engineering: resistance = friction, capacitance = potential energy (spring), inductance = potential energy (opposing spring). These are all terms that are related through the mass and energy equations that tie all engineering areas together.

 

[Loren Pechtel]

While I don't know enough of the math to confirm/deny what you are saying it makes very good sense. I am not in the least surprised that similar phenomenon are described by the same equation in very different realms.

I remember reading a short story long ago. It was set on a large, low gravity world with permanent cloud cover and a pangea landmass. There was this scientist noting some very strange behavior--long distance train tracks didn't have the expected length and mass declined as trains got very fast. His description of things looked very much like some stuff from special relativity. While I didn't actually check the author's math it definitely seemed right--but he was actually describing a curved planet rather than a curved spacetime and the effects of moving at a noticeable percentage of orbital velocity.

 

[steve_bank]

I attended a presentation by a guy designing equipment to evaluate athletes in part during a rehab.

On was a balance board. A balance board is kept level with pins on the ends. You stand on it and the pins are pulled back. As you try and achieve balance the position of the board was electronically recorded.

The plots he showed were damped decaying sine waves as balance was approached. A classical 2nd order system response. Like a parallel RLC electric circuit. I grinned when I saw it.

It took a few years on the job for it to sink in. From a thermodynamics perspective all systems are the same form or model. Once I got that things got easier to understand.

A spring shock absorber system on a car and an RLC cirucit are essentially the same. Energy goes back and forth between two forms.

Or a mass on vertical spring. Lift the mass and let go. Plot the position of mass about equilibrium point and it will be a damped sine wave, same as an RC circuit. Energy goes back and forth from a compressed spring and gravitational potential energy. Energy is lost on each cycle by friction.