Physics: Normal Modes

A normal mode of a dynamical system is a pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation. The free motion described by the normal modes takes place at fixed frequencies. These fixed frequencies of the normal modes of a system are known as its natural frequencies or resonant frequencies. A physical object, such as a building, bridge, or molecule, has a set of normal modes and their natural frequencies that depend on its structure, materials and boundary conditions.

• 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.