In simple harmonic motion (SHM), an object oscillates back and forth around an equilibrium position. A key feature of SHM is the restoring force that acts to bring the object back to this equilibrium position. According to Hooke's Law, the restoring force [tex]\(F\)[/tex] is directly proportional to the displacement [tex]\(x\)[/tex] from the equilibrium position. This relationship is mathematically expressed as:
[tex]\[ F = -kx \][/tex]
Where:
- [tex]\(F\)[/tex] is the restoring force.
- [tex]\(k\)[/tex] is the spring constant (a measure of the stiffness of the spring).
- [tex]\(x\)[/tex] is the displacement from the equilibrium position.
- The negative sign indicates that the force is directed opposite to the displacement.
Given the options:
1. Tension: Tension generally applies to forces experienced by objects like ropes and strings when they are pulled tight. It is not inherently related to the restoring force in simple harmonic motion.
2. Velocity: Velocity is the rate of change of an object's position with respect to time. While velocity is an important aspect of SHM, the restoring force is not proportional to the velocity but to the displacement.
3. Displacement: Displacement is the distance and direction from the object's equilibrium position to its current position. According to Hooke's Law, the restoring force in SHM is directly proportional to the displacement.
4. Period: The period is the time it takes for the object to complete one full cycle of motion. While it characterizes the motion, it does not directly relate to the restoring force's proportional relationship in SHM.
Therefore, the correct answer is displacement. The restoring force in simple harmonic motion is proportional to the displacement from the equilibrium position.
