Page 95 - LAPLACE TRANSFORM

d i(t) = 27 e − ( 9√5 ) sin √5t + ( 3√5 ) cos √5t
-3t
dt 14 14 14

d i(t) = 27 e -3(0.1) − ( 9√5 ) sin √5 (0.1) + ( 3√5 ) cos √5 (0.1)
dt 14 14 14

= 1.429 − (0.006) + (0.048)

= 1.471 Amps

VL (t) = L ( )

= (4) (1.471)

= 5.884 Volts

Calculate the value of VC (t) when t = 0.1sec

−9 -3t 9 3
i(t) = e + cos √5t + sin √5t
14 14 14

t
-3t
∫ i(t)dt = −0.643 e + 0.643 sin √5t − 0.214 cos √5t
0 (−3) √5 √5

= −0.643 e -3(0.1) + 0.643 sin √5(0.1) − 0.214 cos √5 (0.1)
(−3) √5 √5

= 0.159 + 1.122 − 9.563

= 0.150 Amps

1
t
VC (t) = ∫ ( )dt
C 0
1
= (0.150)
50m

= 3 Volts

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