Differential Equations Lecture Work Solutions 12

Differential - − 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

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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 Kircho±’s law. b. Di±erentiate the ²rst equation with respect to t and the second with respect to x i xt + Cv tt + Gv t =0 v xx + Li tx + Ri x =0 Solve the ²rst for i xt and substitute in the second i xt = Cv tt Gv t v xx CLv tt
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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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This note was uploaded on 12/22/2011 for the course MAP 2302 taught by Professor Bell,d during the Fall '08 term at UNF.

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