Which of the following expressions correctly represents Hooke's Law for an ideal spring? 

Explanation:

Hooke's Law for an Ideal Spring

F = -kx

Where:

• F is the restoring force exerted by the spring.
• k is the spring constant, a measure of the stiffness of the spring.
• x is the displacement of the spring from its equilibrium position.

The negative sign indicates that the force exerted by the spring is in the opposite direction to the displacement, meaning that the spring resists deformation and always acts to restore the system to its equilibrium position.

Applications:

• Mechanical Systems: Hooke's Law is widely used in mechanical systems where springs are utilized for shock absorption, vibration damping, and maintaining tension.
• Structural Engineering: In structural engineering, Hooke's Law helps in analyzing the load-bearing capacity and flexibility of materials used in construction.
• Physics Experiments: It is also fundamental in physics experiments that involve measuring forces and displacements, such as in the study of harmonic oscillators.