Therefore, Hooke’s law describes and applies to the simplest case of oscillation, known as simple harmonic motion.įigure 5.40 (a) The plastic ruler has been released, and the restoring force is returning the ruler to its equilibrium position. Recall that Hooke’s law describes this situation with the equation F = − kx. The simplest oscillations occur when the restoring force is directly proportional to displacement. It is then forced to the left, back through equilibrium, and the process is repeated until it gradually loses all of its energy. However, by the time the ruler gets there, it gains momentum and continues to move to the right, producing the opposite deformation. Once released, the restoring force causes the ruler to move back toward its stable equilibrium position, where the net force on it is zero. The deformation of the ruler creates a force in the opposite direction, known as a restoring force. Consider, for example, plucking a plastic ruler to the left as shown in Figure 5.40. Without force, the object would move in a straight line at a constant speed rather than oscillate. Newton’s first law implies that an object oscillating back and forth is experiencing forces. One of the most common uses of Hooke’s law is solving problems involving springs and pendulums, which we will cover at the end of this section.įigure 5.39 A ruler is displaced from its equilibrium position.
The units of k are newtons per meter (N/m). A stiffer system is more difficult to deform and requires a greater restoring force. The larger the force constant, the stiffer the system. The force constant k is related to the stiffness of a system. In the absence of force, the object would rest at its equilibrium position. It is a change in position due to a force.
The deformation can also be thought of as a displacement from equilibrium. Note that the restoring force is proportional to the deformation x. The restoring force is the force that brings the object back to its equilibrium position the minus sign is there because the restoring force acts in the direction opposite to the displacement. Where x is the amount of deformation (the change in length, for example) produced by the restoring force F, and k is a constant that depends on the shape and composition of the object.
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