normal mode
where T denotes kinetic energy and V denotes potential energy. Here ω1, ω2, …, ωn are the natural frequencies of the system. The normal modes of the system are given by qk(t) = Akcos(ωkt + εk) with all other qj being 0.
For a simple light pendulum of length l with a mass m at the end, performing small oscillations about the downward vertical θ = 0, then
Thus, the normal coordinate is 
and the natural frequency is 
For a string y(x,t) fixed at y(0,t) = y(l,t) = 0 and performing small transverse oscillations, there are infinitely many degrees of freedom and the normal modes are
and the corresponding natural frequency is kπc/l. Here c2 = T/ρ where T is the tension in the string and ρ is its density.
- Hessian
- heteroscedastic
- heuristic
- hexadecimal representation
- hexagon
- hexagram
- hexahedron
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- higher arithmetic
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- Hilbert, David
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- holomorphic
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