C16-activities - ACTIVITY 16-1 R = 20 ACTIVITY 16-1 L =.5 H...

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1 ACTIVITY 16-1 s v y + R 20 = Ω L .5 H = C 1 1 1 C F, F, F 250 200 150 = 2 2 0 2 0 Characteristic Equation s 2 s 0 R 1 ; 2L LC α ω α ω + + = = = ACTIVITY 16-1 2 20 20; 400 2(.5) α α = = = 2 2 0 2 2 1 2 0 10t 30t N 1 2 1 C F: 150 300 ; s ,s 10, 30 y K e K e ω α α α ω = = < = − ± = − => = + Overdamped 2 Decaying Exponentials ACTIVITY 16-1 2 2 0 1 2 20t 20t N 1 2 1 C F: 200 400 ; s ,s 20 y K e K t e ω α α = = = = − = − => = + Critically Damped ACTIVITY 16-1 Decaying exponential exponentially damped ramp + 2 2 2 2 0 0 1 2 20t N 1 C F: 250 500 ; 10 s ,s j 20 j10 y A e cos (10t ) ω α β ω α α β φ = = > = = = − ± = − ± => = + Underdamped Sinusoid with exponentially decaying amplitude ACTIVITY 16-1 ACTIVITY 16-2a in v (t) 10u(t) = R 1 H 1 F 400 L .1v L v + i(t) C v + Find i(t)
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