a) A spring has a mass of 2 units, a damping constant of 6 units, and a spring constant of 30 units. If the spring is extended 2 units and then released with a velocity of 2 units. A forcing function of 82(t) is applied to the spring. Answer the following. 2x" + 6x' + 30x= $2(t) x(0) = 2; x'(0) =2 We know 62 (t) = en-2s/s b) A RLC circuit has L = 1 unit, R = 6 units, and C = 1/5 units with E' (t) = 62(t). Given that I'(0) = 1 unit and I(0) = 2 units answer the following. 1) Write the differential equation with the initial values. 2) Find the current I when t = 2 3) What is the limit of I(t) as tend tends to infinity? I'' + 61' + 1/51 = 62(t). We know 62(t) = e^-2s/s