In the metric system, we have g=9.8 m/sec 2.Īccording to Hooke’s law, the restoring force of the spring is proportional to the displacement and acts in the opposite direction from the displacement, so the restoring force is given by -k(s+x). Metric system units are kilograms for mass and m/sec 2 for gravitational acceleration. Recall that 1 slug-foot/sec 2 is a pound, so the expression mg can be expressed in pounds. The acceleration resulting from gravity is constant, so in the English system, g=32 ft/sec 2. In the English system, mass is in slugs and the acceleration resulting from gravity is in feet per second squared. Displacement is usually given in feet in the English system or meters in the metric system.Ĭonsider the forces acting on the mass. Thus, a positive displacement indicates the mass is below the equilibrium point, whereas a negative displacement indicates the mass is above equilibrium. Note that for spring-mass systems of this type, it is customary to adopt the convention that down is positive. Let x(t) denote the displacement of the mass from equilibrium.
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