(1 point) This problem concerns the electric circuit shown in the figure below. Capacitor Resistor Inductor A charged capacitor connected to an inductor causes a current to flow through the inductor until the capacitor is fully discharged. The current in the inductor, in turn, charges up the capacitor until the capacitor is fully charged again. If Q(t) is the charge on the capacitor at time t, and I is the current, then I = do dt If the circuit resistance is zero, then the charge @ and the current I in the circuit satisfy the differential equation L - dt where C is the capacitance and _ is the inductance, so d2Q L- + - = 0. dt2 Then, just as as a spring can have a damping force which affects its motion, so can a circuit; this is introduced by the resistor, so that if the resistance of the resistor is R, + R- do dt2 dt 1Q = 0. If L = 1 henry, R = 1 ohm, and C = 4 farads, find a formula for the charge when (a) Q(0) = 0 and Q' (0) = 7: Q (t ) = (b) Q(0) = 7 and Q' (0) = 0: Q (t ) = Note: You can earn partial credit on this problem.Previous Problem Problem List Next Problem (1 point) A flexible cable suspended between two vertical supports is hanging under its own weight. The weight of a horizontal roadbed is distributed evenly along the x-axis with the density p = 1.1 Ib/ft. The coordinate system is chosen so that the y-axis passes through the lowest point , and the c-axis is a = 4 ft below 1. If the absolute value of tension force in the cable at point P, is T' = 4, then the initial value problem that governs the shape of the cable is (Use the notation dy/ da for the first derivative) dry dz2 y(0) = d (0) = The solution of this problem is y = y(), where y(