2010Midterm2 - Find v(t for t>0 Hint follow the steps(a(b(c(d(e(f For t>0 find the Thevenin equivalent circuit seen from port a and b For t>0 find

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Find v(t) for t>0 Hint: follow the steps: (a) For t>0, find the Thevenin equivalent circuit seen from port a and b. (b) For t>0, find the characteristic equation, and natural frequencies s 1 , s 2 . (c) Is this an overdamped, critically damped, or underdamped case? (d) Find the transient response v t (t) from initial values. (e) Find the steady-state response v ss (t). (f) Find v(t). Solution (a) For t>0, find the Thevenin equivalent circuit seen from port a and b. R TH =6Ω V TH =-4V
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(b) For t>0, find the characteristic equation, and natural frequencies s 1 , s 2 . s 2 + R L s + 1 LC = 0 s 2 + 6 1 s + 1 0.2 = 0 ° 1 = 1, ° 2 = 5 (c) Is this an overdamped, critically damped, or underdamped case? Overdamped (d) Find the transient response v t (t) from initial values. In overdamped condition, v t (t) = A 1 e s 1 t + A 2 e s 2 t Finding v t (0) : v 0 ± = v t 0 ± + v ss 0 ± = 25V 4V = 21V dv(0) dt = dv t (0) dt + dv ss (0) dt = 0 v ss t ± = 4V So v t 0 ± = A 1 + A 2 = 25
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This note was uploaded on 05/19/2011 for the course BME 311 taught by Professor Zhang during the Spring '08 term at University of Texas at Austin.

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2010Midterm2 - Find v(t for t>0 Hint follow the steps(a(b(c(d(e(f For t>0 find the Thevenin equivalent circuit seen from port a and b For t>0 find

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