(2-a) If the voltage V(t) = 10t + 4 sin(t), solve the differential equation; i.e, find the general solution of i(t) of the resulted non-homogeneous differential equation. What will be the particular solution assuming zero initial conditions? (2-b) Use Laplace Transform to solve the same non-homogeneous differential equation from part (2-b). Assume zero initial conditions, and compare your results here with the particular solution obtained in (2-b).

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Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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Fig. 2 shows a series RLC circuit.
V (t)
R
C
5000
L
Fig. 2: Series RLC Circuit
By applying Kirchhoff's voltage law, we obtain the second order differential equation:
d²i di i dv
L- +R + =
dt² dt C dt
where L is the inductance, R is the resistance and C is the capacitance. If L = 1 × 10−³ H, R =
200 , and C = 1 × 10-6 F. Answer the following questions:
(2-a) If the voltage V(t) = 10t + 4 sin(t), solve the differential equation; i.e, find the general
solution of i(t) of the resulted non-homogeneous differential equation. What will be the
particular solution assuming zero initial conditions?
(2-b) Use Laplace Transform to solve the same non-homogeneous differential equation from
part (2-b). Assume zero initial conditions, and compare your results here with the
particular solution obtained in (2-b).
Transcribed Image Text:Fig. 2 shows a series RLC circuit. V (t) R C 5000 L Fig. 2: Series RLC Circuit By applying Kirchhoff's voltage law, we obtain the second order differential equation: d²i di i dv L- +R + = dt² dt C dt where L is the inductance, R is the resistance and C is the capacitance. If L = 1 × 10−³ H, R = 200 , and C = 1 × 10-6 F. Answer the following questions: (2-a) If the voltage V(t) = 10t + 4 sin(t), solve the differential equation; i.e, find the general solution of i(t) of the resulted non-homogeneous differential equation. What will be the particular solution assuming zero initial conditions? (2-b) Use Laplace Transform to solve the same non-homogeneous differential equation from part (2-b). Assume zero initial conditions, and compare your results here with the particular solution obtained in (2-b).
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