Equation 1 · Part 13 · The Machine Before Electronics

Starting index or lower bound: n=1

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

n=1

What this part means

This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.

Its job in the formula

n=1 appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

Full expressionStarting index or lower bound: n=1Article meaning

The passage around this formula

Tides are the response of a rotating, irregularly shaped ocean to the gravitational forcing of the Moon and Sun. The forcing is not one periodic term but many, because the relevant astronomical cycles — lunar day, solar day, lunar month, the inclination of the orbits, the precession of the lunar nodes — beat against one another. The insight that made mechanical prediction 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…

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Learn the underlying idea

Σ adds a collection of terms. Π multiplies them. The lower and upper labels tell you which terms belong to the collection.

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Sources cited in the article section

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