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hw1-s10 - C(s 3 Solve the following differential equations...

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ECE 382 Homework 1 Due: Friday, January 15, 2010 1) The switch has been open for a long time before it is closed at t = 0 . + _ v 1 i 1 E t=0 C 1 R 1 R 2 i 2 C 2 + _ v 2 a) Find v 1 (0 + ) , v 2 (0 + ) , i 1 (0 + ) , and i 2 (0 + ) . b) Find a second-order differential equation satisfied by v 2 ( t ) for t > 0 . 2) Determine the differential equation that describes the system below. If r ( t ) = 3 te - 2 t u ( t ) , where u ( t ) is the unit step function, solve the differential equation using Laplace Transform approach (assume all the initial conditions are zero). 1 s 2 + 3s + 2
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Unformatted text preview: C(s) 3) Solve the following differential equations, where u ( t ) is the unit step function. a) ¨ x + 2 ˙ x + x = 10 tu ( t ); x (0) = 1 , ˙ x (0) = 0 b) ¨ x + 2 ˙ x = (5 + 2 t ) u ( t ); x (0) = ˙ x (0) = 1 c) d 3 x dt 3 + 3¨ x + 3 ˙ x + x = 3 t 2 e-t u ( t ); x (0) = ¨ x (0) = 0 , ˙ x (0) = 2 d) ¨ x ( t ) + 3 ˙ x ( t ) + 2 x ( t ) = (2 e-t + 3 te-2 t ) u ( t ) , x (0 + ) = 1 , ˙ x (0 + ) = 1...
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