Orthogonal harmonic vibrations trace closed Lissajous curves revealing component motion

Evidence

Suppose a small white dot is painted on another body vibrating at right angles to the vibration of the fork and to the axis of the microscope. Viewing this through the microscope, we will see the result of both the dot vibration and the lens vibration. The lens, attached to the tine, executes a simple harmonic oscillation of known frequency. Now a question arises: what is the track taken by the small white dot when viewed through the microscope? It is clear that if the period of the second vibration is the same as that of the prong, the dot will trace a closed curve. If the second vibration is also harmonic, this curve will be an ellipse. If the period is the same as the prong but the second vibration is not harmonic, the curve traced will be more complex. When analyzed, however, the curve obtained will yield the secret of the motion of the second vibration. — Eric J. Heller, Why You Hear What You Hear- An…, 316

Categorization

• XREF: Connects to Lissajous figures and the whole chapter’s core idea that compound motion decomposes into sinusoidal components; bears on Fourier’s theorem introduced elsewhere in the book.
• DEFINE: Explains how Lissajous patterns work mechanically: two orthogonal harmonic oscillations compound into a closed ellipse or more complex curve.