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Consider a simple series RLC circuit with the following values for the resistance, inductance, and capacitance:...

Consider a simple series RLC circuit with the following values for the resistance, inductance, and capacitance: R = 110 Ω (ohms), L = 1 H (henries), and C = 0.001 F (farads). Furthermore, a battery provides an external voltage, e(t), into the circuit equal to 7 However, this external voltage e(t) is not always flowing into the circuit. Initially, the switch for the circuit is open and there is no charge or current flowing through the circuit. At time t = 0, the switch closes and remains closed for exactly 2 seconds, then the switch is re-opened again indefinitely.

  1. Set up an appropriate second order IVP for the charge q(t) in the circuit at any time t, where time is in seconds. Ensure that all units make sense term by term before proceeding. Include the initial conditions for your IVP and describe what each of them represent.

  1. Transform your second order IVP into the algebraic domain, and find the equation for q(t) in Laplace space.

  1. Find the solution for q(t) in the t-domain by computing an inverse Laplace transformation for your answer in b). Next, write your solution in terms of a piecewise function. Lastly, determine the current i(t) in the circuit at any time t in terms of a piecewise function.
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