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fb3_24 - PROBLEM 3.24 KNOWN RCLeircuitzL 2H;C = 1pF;R 101m...

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Unformatted text preview: PROBLEM 3.24 KNOWN: RCLeircuitzL - 2H;C = 1pF;R - 101m 1350) - 1 + 055in2000t v 1(0) - d1(0)/dt = o ASSUMPTIONS: Values for R, C, L remain constant. FIND: Governing equation and steady output form SOLUTION For a single loop RCL circuit, we apply the voltage law to the RCL loop, ER+EC+EL‘Ei(t) fie But, C: L ER =IR: EL =Ld1/dt; EC =(1/cmdt Substituting back into the [cap equation and differentiating once gives, LdZI/dtZ + R dt/dz + (l/C)l - dEi/dt This is of the form for a second order system. It follows that wn = (Ill-R)”; c = R/2(LC)°5; K - 1/C can = 707md/s; : =354;K=1110‘6 From equations 3.21 and 3.19, respectively with w I 2000 rad/s, M(2000 rad/s) = 0.05 “2000 rad/s) = —1.23 rad Then, ”6“» ER.) -. [coo $ivx 1990 t Hammad, s 1 + 0.025 sin(20001- 1.25) m ...
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