Find the charge q(t) on the capacitor and the current i(t) in the given LRC-series circuit. 5 h, R = 10 0, C = - f, E(t) = 800 V, q(0) = 0 C, i(0) = 0 A q(t) = d'q + 8. ag + 329=160 dt C X = A Find the maximum charge on the capacitor. (Round your answer to three decimal places.) CA mass of 1 slug is attached to a spring whose constant is 5 lb/ft. Initially, the mass is released 1 foot below the equilibrium position with a downward velocity of 5 ft/s, and the subs takes place in a medium that offers a damping force that is numerically equal to 2 times the instantaneous velocity. (a) Find the equation of motion if the mass is driven by an external force equal to f(t) = 12 cos 2t + 3 sin 2t. X\") = e_tcos(2t) + 6 sin(2t) ft X A mass weighing 16 pounds stretches a spring % feet. The mass is initially released from rest from a point 4 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to i the instantaneous velocity. Find the equation of motion x(t) if the mass is driven by an external force equal to fit) = 20 cos(3t). (Use 2 g = 32 ft/s2 for the acceleration due to gravity.) X(t) = 47cos(2t) ft X A mass weighing 20 pounds stretches a spring 6 inches. The mass is initially released from rest from a point 3 inches below the equilibrium position. (a) Find the position x of the mass at the times t = \"/12, \"/8, \"/6, \"/4, and 9n/32 5. (Use 9 = 32 ft/s2 for the acceleration due to gravity.) X(7r/12) = (0.125) ft q/ X(7r/8) = 0.25 ft '1 x(7t/6) = O.125 ft 4 1 x(n/4) = Z ft q/ X(97r/32) = T2 ft X (b) What is the velocity of the mass when t = 375/16 s? 2 ft/s V In which direction is the mass heading at this instant? downward O upward q! (c) At what times does the mass pass through the equilibrium position? [M] ,n=o,1,2,... 16