Math 333 Logarithms Worksheet With Answers Page 8
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13(b) Now assume an impressed voltage (varying with time) given by
E(t) = 20 cos ωt.
For what value of ω will the circuit’s steady-state response be the greatest? What
is the maximum voltage drop across the capacitor when this value of ω is used?
Give exact values and decimal approximations.
Solution: Once again we go to p. 203. For this problem, we find that ω
=
0
4
10
5
= 400 10. With γ = 10, we get
2
10
2
5
ω
= 4
10
max
2/16
5
= 4
10
800
so that the maximum response occurs when
ω =
4
10
5
800
631.823 radians per second.
With this value of ω, the amplitude of the response is
20
R
=
max
2
10
10 4
10
5
1
5
10
1
=
.
30 111
The maximum voltage drop across the capacitor is 1/C times this value. That is,
5
10
316.386 volts.
20 111
C1. Use variation of parameters to find the general solution to the differential equation
y + 4y = sec 2t.
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