Final answer:
A linear restoring force is directly proportional to the displacement from equilibrium and acts in the opposite direction. This relationship is explained by Hooke's Law and results in simple harmonic motion for systems like springs and pendulums under certain conditions.
Step-by-step explanation:
In physics, a linear restoring force is one that is directly proportional to the displacement from an object's equilibrium position but acts in the opposite direction. When a system obeys Hooke's law, the magnitude of the restoring force can be represented by F = -k * d, where 'F' is the restoring force, 'k' is the force constant, and 'd' is the displacement from equilibrium. The negative sign indicates that the force is in the opposite direction to the displacement. The force constant, 'k', represents the rigidity or stiffness of the system, with a larger 'k' indicating a stiffer system, and is expressed in newtons per meter (N/m). If an object like a mass attached to a spring or a simple pendendulum exihibits this proportional relationship between displacement and restoring force for small displacements (such as angles less than 15° for pendulums), it will perform simple harmonic motion, with an oscillation frequency that is independent of amplitude but dependent on the square root of the force constant and the inverse square root of the mass.