Hello Forum,
The 1D harmonic oscillator is an important model of a system that oscillates periodically and sinusoidally about its equilibrium position. The restoring force is linear. There is only one mode with one single frequency omega_0 (which is the resonant frequency).
What about the 2D oscillator? are a vibrating drum membrane or a rectangular membrane an examples of 2D harmonic oscillator? In that case there are many modes, each having a frequencies that is an integer multiple of the fundamental frequency omega_0, correct? Also each mode has a sinusoidal temporal behavior at every point in space even if the full spatial dependence is not sinusoidal (Bessel functions for circular membrane)...
So, in going from 1D to 2D, we go from having one mode to having countably infinite modes because we go from one degree of freedom to infinite (why countable if the membrane is made of infinite points? The DOF should be infinite) degrees of freedom.
thanks,
fog37
The 1D harmonic oscillator is an important model of a system that oscillates periodically and sinusoidally about its equilibrium position. The restoring force is linear. There is only one mode with one single frequency omega_0 (which is the resonant frequency).
What about the 2D oscillator? are a vibrating drum membrane or a rectangular membrane an examples of 2D harmonic oscillator? In that case there are many modes, each having a frequencies that is an integer multiple of the fundamental frequency omega_0, correct? Also each mode has a sinusoidal temporal behavior at every point in space even if the full spatial dependence is not sinusoidal (Bessel functions for circular membrane)...
So, in going from 1D to 2D, we go from having one mode to having countably infinite modes because we go from one degree of freedom to infinite (why countable if the membrane is made of infinite points? The DOF should be infinite) degrees of freedom.
thanks,
fog37
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