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It's just a casual observation, so I wanted to check it: A regular spring, when not completely compressed, looks an awful lot like a sine wave. The idea of a circular shape stretched out in the third dimension also seems to support it. But I can find no mention anywhere that such a spring actually is (or isn't) shapes like a sine wave. I don't want to tell my pupils this unless it is more than just an observed similarity. So is a stretched spring, if seen from the side, shaped like a sine wave?

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    $\begingroup$ I don't understand the question. What do you mean by a spring being "shaped like a sine wave"? $\endgroup$
    – ACuriousMind
    Apr 18, 2016 at 0:10
  • $\begingroup$ I believe he means the projection of the spring onto a plane that cuts through the center $\endgroup$
    – zeldredge
    Apr 18, 2016 at 0:11
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    $\begingroup$ A "regular spring" is usually a coil spring and it is shaped like a helix. There are sine and cosine in the description of that shape, which, when seen in projection from a direction perpendicular to the axis of the spring can show up (but only approximately). $\endgroup$
    – CuriousOne
    Apr 18, 2016 at 0:13

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Your casual observation is astute; there is a relationship between the coils of a spring and sinusoids:

$$e^{ix} = \cos x + i \sin x $$ enter image description here

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A typical wound-into-a-cylinder spring is a helical in shape.

And yes that means that subjected to tension and viewed from the side the transverse displacement will be sinusoidal to the same precision with which it approximates a helix.

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The question is referring to an over-stretched coil viewed from the side. I would say yest it resembles a wavey shape but I’m not sure of the wave,s properties.

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