PH2230 - Laplace Transform
HW5
1) For the circuit below, the switch has been open for a long time. The switch is then closed at
t = 0. Solve for the current into the capacitor as a function of time using the Laplace transform
method. The sinusoidal voltage source operates at a frequency of 50 Hz.
For the purpose of this exercise, do not use any circuit reduction (e.g. do not create a Thevenin
equivalent for the source and resistors).
(Remember that all grounds are connected together).
Some Laplace Transform Pairs
f(t)
F(s)
1.
1
1/s
2.
t
1/s2
3.
e-at
1/(s+a)
4.
te-at
1/(s+a)2
5.
sin(ωt)
ω/(s2+ω2)
6.
cos(ωt)
s/(s2+ω2)
7.
e-at sin(ωt)
ω/[(s+a)2+ω2]
8.
e-at cos(ωt)
(s+a)/[(s+a)2+ω2]
9.
sinh(ωt)
ω/(s2-ω2)
10.
cosh(ωt)
s/(s2-ω2)
11.
df
dt
s F(s) - f(0+)
∫ f (τ ) dτ
F(s)/s
t
12.
0
13.
14.
c1 f1(t) + c2 f2(t)
∫f
1
(τ ) f 2 (t − τ ) dτ
c1 F1(s) + c2 F2(s)
F1(s) F2(s)