18.03 Lecture Notes - Lecture 17: Rlc Circuit, Linear Time-Invariant Theory, Inductor
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[1] we"ve spent a lot of time with mx" + bx" + cx = q(t) . There are many other systems modeled by this equation. V = voltage increase across the power source. V_r = r i v_c" = (1/c) i. Differentiate kvl : v_r" + v_c" = v" so r i" + (1/c) i = v" In lecture 3 we offered this as an example of a first order lti system. The voltage drop across an inductor depends not on the current but rather on the derivative of the current: V_l = l i" so v_l" = l i" . Kvl now says v_l + v_r + v_c = v so l i" + r i" + (1/c) i = v" (*) [2] suppose you want to solve u" - 4u = cosh(2t) Remember, i can write the left hand side as p(d) u where p(s) = s^2 - 4 .
R2=10.000 
