Equation 1 · Part 7 · The Machine Before Electronics

Symbol omega_n

h(t) = H_0 + \sum_{n=1}^{N} A_n \cos(\omega_n t + \phi_n)

\omega_n

What this part means

a known astronomical angular frequency.

Its job in the formula

omeg $a_n$ is one of the signed contributions combined to compute the quantity on the left.

Full expressionSymbol omega_nArticle meaning

Where the article explains it

Here $\omega_n$ is a known astronomical angular frequency, while $A_n$ and $\phi_n$ are constituents determined by fitting the expression to a record of observed water levels at that specific place.

The passage around this formula

…possible was that the local water level can be written as a constant plus a sum of sinusoids whose frequencies are fixed by astronomy and whose amplitudes and phases are fixed by the harbour: $h(t) = H_0 + \sum_{n=1}^{N} A_n \cos(\omega_n t + \phi_n)$ . Here $\omega_n$ is a known astronomical angular frequency, while $A_n$ and $\phi_n$ are constituents determined by fitting the expression to a record of observed water levels at that specific place. The division of labour is the whole trick. The frequencies are universal and can be built into gearing once.…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the article section

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