3. Consider the electric circuit shown in Figure 3. (a) Determine the differential equation relating input r(t) to output y(t). (b) Determine the output y(t) in response to the input x (t) = 4te-3t/2u(t). Assume component values of R = 1, C₁ = 1F, and C₂ = 2F, and initial capacitor voltages of Vc₁ = 2V and Vc₂ = 1V. Note: this is a more difficult problem. x(t) R ww C₁ y(t) Figure 3: RCC circuit. + C₂

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3. Consider the electric circuit shown in Figure 3.
(a) Determine the differential equation relating input r(t) to output y(t).
(b) Determine the output y(t) in response to the input x(t) = 4te-³t/²u(t). Assume component values
of R = 1, C₁ = 1F, and C₂ = 2F, and initial capacitor voltages of Vc₁ = 2V and Vc₂ = 1V.
Note: this is a more difficult problem.
x(t)
R
m
C₁
y(t)
Figure 3: RCC circuit.
C₂
Transcribed Image Text:3. Consider the electric circuit shown in Figure 3. (a) Determine the differential equation relating input r(t) to output y(t). (b) Determine the output y(t) in response to the input x(t) = 4te-³t/²u(t). Assume component values of R = 1, C₁ = 1F, and C₂ = 2F, and initial capacitor voltages of Vc₁ = 2V and Vc₂ = 1V. Note: this is a more difficult problem. x(t) R m C₁ y(t) Figure 3: RCC circuit. C₂
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