(a) The circuit shown in Figure is a model of a solenoid, such as that used to engage the gear of a car's starter motor to the engine's flywheel. The solenoid is constructed by winding wire around an iron core to make an electromagnet. The resistance R is that of the wire, and the inductance L is due to the electromagnetic effect. When the supply voltage vs is turned on, the resulting current activates the magnet, which moves the starter gear. Obtain the model of the current i given the supply voltage vs.
(b) Suppose vs(t) = Vus(t) and i(0) = 0. Obtain the expression for the response for i(t).

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