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- Dictionarysubharmonic/ˌsʌbhɑːˈmɒnɪk/
noun
- 1. an oscillation with a frequency equal to an integral submultiple of another frequency.
adjective
- 1. denoting or involving a subharmonic.
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A subharmonic function is a class of functions related to convex functions and harmonic functions in mathematics. Learn the definition, properties, examples and applications of subharmonic functions in Euclidean space, complex analysis and Riemannian manifolds.
The oscillations of a pendulum with \ (\ \delta / \omega_ {0}=0.03\), driven by a sinusoidal external force of amplitude \ (\ f_ {0}=3\) and frequency \ (\ 0.8 \times 3 \omega_ {0}\), at initial conditions \ (\ q (0)=0\) (the top row) and \ (\ q (0)=1\) (the bottom row), with \ (\ d q / d t (0)=0\) in both cases.
We will consider harmonic and subharmonic functions in \(\mathbb{C} \cong \mathbb{R}^2\). Let us go through some basic results on harmonic and subharmonic functions in \(\mathbb{C}\) that you have seen in detail in your one-variable class.
Undertone series or subharmonic series is a sequence of notes that results from inverting the intervals of the overtone series. Learn how to produce subharmonics in music, voice, instruments and electronics, and how they differ from harmonics and overtones.
Jan 23, 2021 · 2) The upper envelope $ \sup \ { {u _ {k} ( x) } : {1 \leq k \leq m } \} $ of a finite family of subharmonic functions $ \ { u _ {k} \} _ {k=1} ^ {m} $ is a subharmonic function. If the upper envelope of an infinite family of subharmonic functions is upper semi-continuous, then it is also a subharmonic function.
May 29, 2023 · Subharmonic frequencies are frequencies below the fundamental frequency of an oscillator in a ratio of 1/n, with n a positive integer. For example, if the fundamental frequency of an oscillator is 440 Hz, sub-harmonics include 220 Hz ( 1⁄2), ~146.6 Hz ( 1⁄3) and 110 Hz ( 1⁄4).
A subharmonic is a component of a periodic wave which has a frequency lower than the declared fundamental. As an example, a component with half the frequency of the fundamental would be the second subharmonic, and whereas the harmonic series are defined by the arithmetic multiplication of the fundamental frequency, subharmonics involve the ...
