#### (Solved): (1 Point) A Mass Weighing 4 Lb Stretches A Spring 18 In. From Equilibrium, The Mass Is Displaced An ...   (1 point) A mass weighing 4 lb stretches a spring 18 in. From equilibrium, the mass is displaced an additional 4 in downward and then released with an upward velocity of 16 ft/sec. Assuming that there is no damping and that the mass is acted on by an external force of 0.125 cos 5t lb, formulate but DO NOT SOLVE the initial value problem describing the motion of the mass. u"!) + u'(t) + u(t) = (0) = ft, u'(0) = ft/sec. (1 point) A mass weighing 1.5 kg stretches a spring 20 cm. From equilibrium, the mass is displaced an additional 20 cm in the upward direction and then released with a downward velocity of 1 m/sec. The mass also moves in a medium that imparts a viscous force of 6 N when the speed of the mass is 3 m/sec. Assuming that the mass is acted on by an external force of 1.5 sin 41 N, formulate but DO NOT SOLVE the initial value problem describing the motion of the mass. u"(t) + u' (t) + u(t) = u(0) = m, ?(0) = m/sec. (1 point) A mass weighing 0.75 kg stretches a spring 50 cm. The mass is pulled downward an additional 40 cm and then released. The mass is also attached to a dashpot mechanism which imparts a force of 18 N when the speed of the mass is 3 m/sec. Assuming that the mass is acted on by an external force of 2.25e-7 N, formulate but DO NOT SOLVE the initial value problem describing the motion of the mass. Use g = 9.8 m/sec. u"(t) + u'(t) + u(t) = (O) = m, u (0) = m/sec.