# Π sin 2 n 1 πx t where v is the value of the on

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π sin (2 n - 1) πx T Where v 0 is the value of the on state of the square wave and T is the period of the wave. Thus, we expect the particular solutions for the sine wave to be some linear combination of sine and cosine, such as Q = A sin ωt + B cos ωt for some values of A and B, satisfying the differential equation. similarly, we expect the particular soltuion for the square wave to be an infinite summation of such sines and cosines, with an additional constant term corresponding to v 0 2 . However, we will not go into such a derivation here. 3

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2 Data Here are some pictures of each regime. The sinusoidal portion represents the underdampened case, in which the sine and cosine terms exist. 4
The bump shows the closest values that correspond to the critically dampened case, because the R, L, and C values do not match perfectly. However, this was the first data point after the trigonometric terms drop out. This is just a straight exponentially decreasing graph, corresponding to the 5

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overdampened case. 3 Analysis and Results RLC circuits are a thing. Like cats. Cats are cute. See? Say hi to Damian, kitty! 6
• Winter '13
• MarceloGleiser
• Physics, Electronics, Square wave, Elementary algebra, Sine wave, RLC Circuits

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