Learning Goals
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- Explain what a normal mode is.
- Define the frequency, amplitude, and phase of a normal mode.
- Explain why different normal modes have different frequencies and why higher-numbered modes have higher frequencies.
- Identify how many normal modes a given system has.
- Sketch the individual modes qualitatively for both 1D and 2D systems.
- Explain the distinction between transverse and longitudinal normal modes in a 1D system.
- Explain how adjusting the phase of a normal mode affects the motion of the system.
- Explain qualitatively how any arbitrary state of the system can be written as a sum of normal modes; that is, explain the superposition principle.
- Explain which properties of the system are set by the initial conditions, which properties are time-independent, and which properties are time-dependent.
- Explain why striking a metal plate in one spot raises the temperature of the plate.