Find the solution of the given initial value problems y" 2}\" + J? = tat + 4 with Jim] = 1 and y'f} = 1 y" + zy' + 53; = te'i cos 2: with you = 1 and y'ED} = o J 1'2 }' _ 1+3.-2 A mass of l g stretches a spring ? cm. If the mass is set in motion from its equilibrium position with a downward velocity of ll] cmf'st and if there is no damping, determine the position it of the mass at any time t. Ilitihen does the mass rst return to its equilibrium position? A mass weighing 3 lb stretches a spring 3 in. If the mass is pushed upward. contracting the spring a distance of 1.5 in, and then set in motion with a downward velocity of 2 ftfst and if there is no damping, nd the position u of the mass at any time t. Determine the freouencys period, amplitude and phase of the motion. A mass weighing 3 lb stretches a spring 1.5 in. The mass is also attached to a damper with coefcient r. Determine the value of y for which the system is critically damped. If a series circuit has a capacitor of C = {LE x l'F and an inductor of L = {LE H nd the resistance it so that the circuit is critically damped. Ifthe Wronskian W offand g is 3a\" and if f) = a\" nd g{t]. A tank initially contains 120 L of pure water. A mixture containing a concentration of y 33" L of salt enters the tank at a rate of 2 Umin, and the well stirred mixture leaves the tank at the same rate. Find an expression in terms of y for the amount of salt in the tank at any time 1'. Also nd lite limiting amount of salt in the tank as t -v oo