A linear spring stores elastic energy when displaced by from its relaxed position. The external force maintaining that displacement is ; its restoring force on the moving attachment has the opposite sign. Its spring constant has units force per length.
The spring constant is the positive proportionality coefficient in the ideal spring restoring force . Its SI unit is newtons per metre. With a constant attached mass , it sets the angular frequency of simple harmonic motion. Doubling doubles the restoring force at a fixed displacement, but increases that angular frequency only by a factor .
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