Equation 1 · Part 6 · The Machine Before Electronics

Symbol A_n

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

A_n

What this part means

the while.

Its job in the formula

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

Full expressionSymbol A_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

…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. The amplitudes and phases are local and must be adjustable.

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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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