Question:
Why is it that only a sinewave can preserve its shape
when it passes through a circuit while no other waveform can?

Replies:
Venkatesh,

A standard circuit has some parts that depend on the current, some that
depend on the rate at which the current changes, and some that depend on the
total effect of the current over time. The rate of change is the slope of
the current. The slope of a sine wave is a cosine wave, which is the same
shape as a cosine wave. The total effect of the current over time is the
area under the current function. For a sine wave, this works out to be the
opposite of a cosine wave. If you add together sine and cosine waves that
have the same frequency, you get a sine wave shifted to the left or right.
A sine wave is the only function to have these properties without getting
steadily larger or steadily smaller.

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