Open the Fourier Series Demo and select the "Arbitrary" function. Which term in the Fourier series representation is responsible for the vertical offset of the Fourier-approximated curve?

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When examining how a Fourier series represents a function, the vertical offset is determined by the constant component of the series. 
Option 1: The initial 5/12 (constant) term. This term acts as the baseline value around which the sine and cosine components oscillate, thereby setting the overall vertical offset of the reconstructed curve. 
Option 2: The sine terms. Sine terms have averages of zero over a full period, so they modulate the shape and symmetry about the axis but do not shift the overall vertical position; they contribute to the waveform’s odd components rather than the offset. 
Option 3: The cosine terms. Except for the very first cosine term that can be related to the constant when considered with a0, higher-order cosine terms have zero average over a full period and primarily shape the even components; they do not create a persistent vertical shift by themselves. 
Option 4: The summation. The Fourier sum combines constant, sine, and cosine parts, but the aggregate offset is specifically set by the constant term; the rest add oscillatory content but do not establish the baseline offset on their own. 
In summary, the constant term provides the vertical offset, while the other components refine the waveform without altering that baseline offset.

AMME2000 BMET2960 BMET9960 (ND) Week 4 Pre-work

Open the Fourier Series Demo and select the "Arbitrary" function. Which term in the Fourier series representation is responsible for the vertical offset of the Fourier-approximated curve?

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