MAE 182 Sample Final Exam

MAE 182 Sample Final Exam - Problem 1 (5+5+10) Consider the...

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Problem 1 (5+5+10) Consider the first order differential equation (DE) ( ) 0 dy ax by bx cy dx where ,, abc are constants. a. Is the above equation linear or nonlinear? Explain your answer. b. Is there an integrating factor () x of the DE? If so, find x . c. Solve the differential equation. Problem 2 (5+5+15) For the electric, series circuit shown, a. find the governing differential equation for the charge qt at time t in the circuit in terms of R , C , L and V ( t ) b. Is the solution of the above differential equation stable or unstable for R, C, L > 0? Recall that a solution is unstable if it becomes unbounded as time t increases. Describe the steady state behavior of the current I ( t ) for R, C, L > 0 and ) cos( ) ( t te t V t volts. c. The circuit above initially starts with no current flowing, and no charge across the capacitor C . Given that R = 3 ohm, C = 1/2 Farad, L = 1 Henry, and t e t V ) ( volts. Solve for the current It as a function of time. Give units. HINT: RI V R (Voltage across resistor) C q V c (Voltage across capacitor) dt dI L V L
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This note was uploaded on 09/11/2008 for the course MAE 182A taught by Professor King during the Spring '08 term at UCLA.

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MAE 182 Sample Final Exam - Problem 1 (5+5+10) Consider the...

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