Demos: 1S-32 SHM Generator

To show that simple harmonic motion is the projection onto a plane of uniform circular motion, an arrow is affixed to a rotating turntable and the arrow’s shadow is projected onto a screen. The length of the shadow represents the amplitude of the SHM and this length changes sinusoidally.

Directions: Turn on the halogen lamp so that the shadow image of the arrow is projected onto the flat screen. The turntable is rotated by means of a hand crank. Make sure that the rotation speed is kept constant. [Note: Because the arrow on the turntable is alternately closer and farther from the light source, the shadow will get bigger and smaller in addition to the changing length. This is usually a minor distraction, but should be pointed out.]

Suggestions for Presentation: The linear projection of circular motion is usually presented abstractly as equations. Remind the students that the term “projection” onto an axis can be thought of as the “shadow” of the vector on a line. Review the fact that the amplitude of the SHM goes from zero to maximum sinusoidally and this is precisely what the arrow shadow is doing on the screen. This helps the student focus on the proper attributes of the demonstration.

Applications: Nothing in real life, but this demo has broader applications to vector projection.

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