Lq" + Rq' + 79 = 0 where q(t) is the charge across the capacitor. (a) By introducing a new variable I = q'(t), rewrite this equation as a system of two first order equations. (b) Suppose L = 1, R = 0 and C = 1/4. If q(0) = 8 and q'(0) = 0, guess a solution q(t).

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Answer all parts

1
Lq" + Rd +
where q(t) is the charge across the capacitor.
(a) By introducing a new variable I = q'(1), rewrite this equation as a system of two first order
equations.
(b) Suppose L = 1, R = 0 and C = 1/4. If q(0) = 8 and q'(0) = 0, guess a solution q(1).
(c) For the solution you found in part (b), show a time series plot (q vs t) as well as a graph of q vs
I in the phase plane.
Transcribed Image Text:1 Lq" + Rd + where q(t) is the charge across the capacitor. (a) By introducing a new variable I = q'(1), rewrite this equation as a system of two first order equations. (b) Suppose L = 1, R = 0 and C = 1/4. If q(0) = 8 and q'(0) = 0, guess a solution q(1). (c) For the solution you found in part (b), show a time series plot (q vs t) as well as a graph of q vs I in the phase plane.
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