An engineering student built a series circuit as shown in the picture. R 12V (If you are curious, here are the specifications of the components used to build this circuit: A resistor with R = 202, an inductor with L 1H, a capacitor with C 0.002F, and a 12V battery). The charge on the capacitor C at time t, is given by Q(t) which solves the differential equation Q" + 20Q' + 500Q = 12 %3| Which of the following describes the general solution of this ODE? Q(t) = e 10t (cj cos 20t + c2 sin 20t) + t 125 Q(t) -10t (C1 cos 20t + c2 sin 20t) = e Q(t) 3 10t (cj cos 20t + c2 sin 20t)+ = e 125 Q(t) = cie20t + c2e20t 3 + 125

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Publisher:Robert L. Boylestad
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An engineering student built a series circuit as shown in the picture.
R
12V
(If you are curious, here are the specifications of the components used to build this circuit:
A resistor with R = 20N, an inductor with L
1H, a capacitor with C
0.002F, and a 12V
battery).
The charge on the capacitor C at time t, is given by Q(t) which solves the differential equation
Q" + 20Q' + 500Q
12
Which of the following describes the general solution of this ODE?
3
Q(t) = e
-10t (cj cos 20t + c2 sin 20t)+
-t
125
O Q(t) = e-10 (c1 cos 20t + c2 sin 20t)
Q(t) = e
3
-10t (cj cos 20t + c2 sin 20t)+
125
Q(t) = ce20t + cze20t
3
+
125
= C1
丰
Transcribed Image Text:An engineering student built a series circuit as shown in the picture. R 12V (If you are curious, here are the specifications of the components used to build this circuit: A resistor with R = 20N, an inductor with L 1H, a capacitor with C 0.002F, and a 12V battery). The charge on the capacitor C at time t, is given by Q(t) which solves the differential equation Q" + 20Q' + 500Q 12 Which of the following describes the general solution of this ODE? 3 Q(t) = e -10t (cj cos 20t + c2 sin 20t)+ -t 125 O Q(t) = e-10 (c1 cos 20t + c2 sin 20t) Q(t) = e 3 -10t (cj cos 20t + c2 sin 20t)+ 125 Q(t) = ce20t + cze20t 3 + 125 = C1 丰
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