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Differential Equations Lecture Work Solutions 12

Differential Equations Lecture Work Solutions 12 - − GL v...

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1. Follow class notes. a , b are the proportionality constants for the forces mentioned in the problem. 2. a. Check any physics book on Kirchoff’s law. b. Differentiate the first equation with respect to t and the second with respect to x i xt + C v tt + G v t = 0 v xx + L i tx + R i x = 0 Solve the first for i xt and substitute in the second i xt = C v tt G v t v xx CL v
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Unformatted text preview: − GL v t + R i x = 0 i x can be solved for from the original ²rst equation i x = − C v t − G v ⇒ v xx − CL v tt − GL v t − RC v t − RG v = 0 Or v tt + G C + R L ± v t + RG CL v = 1 CL v xx which is the telegraph equation. In a similar fashion, one can get the equation for i . 12...
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