After a mass m is attached to a spring, the spring is stretched s units and hangs at rest at the equilibrium position as shown in Figure 1.3.17(b). Then the spring/mass system is set in motion, let x(t) denote the directed distance from the equilibrium point to the mass. As shown in Figure 1.3.17(c), assume that the downward direction is positive and that the motion is on a vertical straight line through the center of gravity of the mass and that the only forces acting on the system are the weight of the mass and the restoring force of the stretched spring. Use Hooke's law: the restoring force of a spring is proportional to its total elongation. Determine a differential equation of the displacement x(t) at time t>0.
After a mass m is attached to a spring, the spring is stretched s units and hangs at rest at the equilibrium position as shown in Figure 1.3.17(b). Then the spring/mass system is set in motion, let x(t) denote the directed distance from the equilibrium point to the mass. As shown in Figure 1.3.17(c), assume that the downward direction is positive and that the motion is on a vertical straight line through the center of gravity of the mass and that the only forces acting on the system are the weight of the mass and the restoring force of the stretched spring. Use Hooke's law: the restoring force of a spring is proportional to its total elongation.
Determine a differential equation of the displacement x(t) at time t>0.
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