5.2.12 (LRC circuit) Consider the circuit equation Li +Rİ + 1/C = 0, where L,C>..." />

5.2.12 (LRC circuit) Consider the circuit equation Li +Rİ + 1/C = 0, where L,C>and R20. a) Rewrite the equation as a two-dimensional linear system. b) Show that the origin is asymptotically stable if R>0 and neutrally stable if R=0. c) Class

匿名用户 最后更新于 2021-12-01 19:14 数学类Mathematics

and R20.a) Rewrite the equation as a two-dime">

5.2.12 (LRC circuit) Consider the circuit equation Li +Rİ + 1/C = 0, where L,C>and R20. a) Rewrite the equation as a two-dimensional linear system. b) Show that the origin is asymptotically stable if R>0 and neutrally stable if R=0. c) Classify the fixed point at the origin, depending on whether R’C-4L is posi- tive, negative, or zero, and sketch the phase portrait in all three cases.

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