If k is the spring’s force constant and x is the displacement from its undeformed position of a spring, then the potential energy (V) of the spring is: 

The correct answer is V = kx² / 2.

Key Points

• The potential energy (V) stored in a spring is given by the formula V = (1/2)kx², where k is the spring constant and x is the displacement from the spring's equilibrium position.
• This formula is derived from Hooke's Law, which states that the force exerted by a spring is proportional to its displacement: F = -kx.
• The potential energy corresponds to the work done in deforming the spring, which is equivalent to the area under the force-displacement curve (a triangle).
• The spring constant (k) represents the stiffness of the spring and is measured in Newton/meter (N/m).
• The displacement (x) is the distance the spring is stretched or compressed from its natural (undeformed) position, measured in meters.

Additional Information

• Hooke's Law:
  • Hooke's Law states that the force exerted by a spring is directly proportional to its displacement: F = -kx.
  • The negative sign indicates that the spring force is restorative, meaning it acts in the opposite direction of displacement.
• Elastic Potential Energy:
  • Elastic potential energy is the energy stored in elastic materials, such as springs, when they are stretched or compressed.
  • This energy is released when the material returns to its equilibrium state.
• Spring Constant (k):
  • The spring constant is a measure of the stiffness of the spring.
  • A higher value of k indicates a stiffer spring, which requires more force to produce the same displacement.
• Work-Energy Theorem:
  • The work done on the spring to compress or stretch it is stored as potential energy.
  • This theorem is the foundation for deriving the formula for the spring's potential energy.