Consider a damped, forced mass/spring system. Let t denote time (in seconds) and let x(t) denote the position (in meters) of the mass at time t, with x = 0 corresponding to the equilibrium position. Suppose the mass m = 1 kg, the damping constant c = 3 N·s/m, the spring constant k = 2 N/m, the external force is F (t) = 20 cos(2t), the initial position x(0) = 1 m, and the initial velocity x′(0) = 2 m/s. a. Find the position function x(t). b. What part of the solution is the transient part and what part is the steady-state part? An RLC circuit contains in series a resistor R = 3 Ω, an inductor L = 1 H, and a capacitor C = 0.5 F. The current I(t) is provided by a source with emf E = 20cos(2t) Volts, where t is the time. Find the steady-state current Ip that develops after a long time (theoretically when t → [infinity]). For the differential equation y′′ + 4y = 2 tan(2x), solve its homogeneous part. Then use variation of parameters to find a particular solution yp.