Consider an RLC circuit with resistance 2 ohms, inductance 0.1 henrys, capacitance 0.004 farads, and an impressed voltage, provided by an alternating current generator, of $\displaystyle {E}{\left({t}\right)}={10}{\sin{{\left({100}{t}\right)}}}$. At $\displaystyle {t}={0}$ the charge is 5 coulomb and the current is 1 amps.

a. Complete the ODE below in terms of the charge in the circuit $\displaystyle {Q}{\left({t}\right)}$

$\displaystyle {Q}{''}$+ $\displaystyle {Q}'$ + $\displaystyle {Q}$ =

b. Solve the ODE and complete the equation for the charge $\displaystyle {Q}{\left({t}\right)}=$

c. Upload a file with your work for part b and a graph of the current I(t)

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d. Interpret the graph of the current in the context of the RLC circuit scenario