Mechanical engineers and electrical engineers have different mental models of oscillation
(Diary of an Old AI Researcher who is still Programming)
30 October 2019
When I was a young associate professor, a professor of flight dynamics
- great Professor K - suddenly came to my office and said,
‘Professor Hori, since your major was electronics, let me ask you a
question. A radio wave of higher frequency has larger energy than a radio
wave of lower frequency. Is this correct?’.
I answered, ‘No, I do not think so, sir, Professor K. If a radio wave
of higher frequency has larger energy than a radio wave of lower frequency,
UHF TV stations should spend more electricity charge
than the VHF TV stations. I have never heard that.’
Professor K continued, ‘But imagine you are in a bath tub.
When you make a water wave of higher frequency by tapping the surface of
the hot water in the bath tub, you get more tired than when you make
a wave of lower frequency. Professor M of fluid dynamics says I am right.’
I was surprised, ‘What? Professor M also says so? OK, let me go to the library
At that time, we did not have the world wide web, yet,
and I went to the library of the
department of electronics.
Of course, there is no relation between the frequency and the energy in radio
waves(*1). I heard afterward that the great professor K was investigating the
problem of intrusion into auto-pilot systems of airplanes.
When I tell this episode while drinking with my colleague professors of
the school of engineering, the reactions are always far stronger than I expect,
and a long argument emerges with laughter.
At first, most of the engineering professors who majored in mechanical
engineering respond ‘I think the great professor K is right!’.
They say, ‘Imagine a mass and a spring. When the mass moves faster,
the mass has more energy. So, the oscillation of higher frequency has larger
I say, ‘No, imagine a simple pendulum. If we give the same initial potential
energy, the oscillations have the same energy independent of the
Isn't this interesting?
The basic mental model of oscillation is the mass-spring system in
engineers' minds, and the basic mental model of oscillation is a simple
pendulum in the electrical engineers' minds.
I have not examined this hypothesis on the engineers' mental models
I believe that you will get the same responses from the engineers if you
tell this episode.
By the way, even in the mass-spring model, the oscillation has the same
energy independent of the frequency if we give the same initial potential
energy, of course. But, in the mechanical engigneers' minds,
the figures of the oscillations of the same amplitude seem to be drawn
If the mass and the amplitude are fixed and the spring constant is
changed, the energy and the frequency will change.
If you like, please confirm the formulae below. :-)
where is energy, is frequency, is
spring constant, is amplitude, and is mass.
Sorry, depending on your browsers, the above formulae may not be shown correctly(*2).
In a plain text, the above formulae are,
E = (1/2)*k*(A squared),
f = (1/2π)*squareroot(k/m).
Moreover, in many cases, resonance is a dangerous phenomenon for mechanical
engineers, while it is a phenomenon positively used for electrical engineers.
(*1) In electromagnetism, the energy density of a radio wave is the
sum of the energy density from the electric field and the
energy density from the magnetic field, which are independent of the
On the other hand, in quantum mechanics, when we consider the
particle nature of electromagnetic radiations, a photon has
the energy of hν, where h is the Planck constant and ν is frequency.
We can say Professor K was right in a sense, focusing on one photon.
(*2) MathML is used. Following is the source html code.
<mi>E</mi> <mo>=</mo> <mfrac><mn>1</mn><mn>2</mn></mfrac><mi>k</mi><msup><mi>A</mi><mn>
<mi>f</mi> <mo>=</mo> <mfrac><mn>1</mn><mrow><mn>2</mn><mi>π</mi></mrow>
© 2019 Koichi Hori