Superposition of normal modes with chosen amplitudes reproduces any shape

Evidence

Any shape can be reproduced as a combination of all the pure modes, if the correct amplitudes are used. We illustrate the superposition in the two-bead case in figure 8.5; it is easy to see exactly how the new shape is created out of two normal modes. A single bead will oscillate at N different frequencies at once if N modes are excited. — Eric J. Heller, Why You Hear What You Hear- An…, 796

Categorization

• XREF: Superposition of modes is the same principle behind Fourier synthesis, which would matter for how any complex sound decomposes into harmonics.
• DEFINE: Defines superposition: combining pure modes with chosen amplitudes yields arbitrary shapes.