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SOLVED: A resistor-inductor-capacitor (RLC) network is depicted in Figure 2LRvc(t)Figure 2: A resistor-inductor-capacitor (RLC) networka) Find the differential equation relating the capacitor voltage, vc(t), to the input voltage, v(t)[5 Marks]Hint: The voltage-current relationships of capacitor, resistor, and inductor areb) Find the transfer function relating the capacitor voltage, Vc(s), to the input volt- age, V(s).[5 Marks]c) Determine the characteristic equation of the control system,if R=2O
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