How is the potential energy of a system in simple harmonic motion calculated?

The potential energy of a system in simple harmonic motion is calculated using the equation U = 1/2 kx^2.

In simple harmonic motion, the potential energy of a system is stored in the spring or elastic material that is being stretched or compressed. The amount of potential energy stored in the system is directly proportional to the amount of displacement from the equilibrium position. This means that the further the system is displaced from its equilibrium position, the greater the potential energy stored in the system.

The equation for the potential energy of a system in simple harmonic motion is U = 1/2 kx^2, where U is the potential energy, k is the spring constant, and x is the displacement from the equilibrium position. This equation shows that the potential energy of the system increases as the displacement from the equilibrium position increases.

The potential energy of a system in simple harmonic motion can also be visualized using a graph of potential energy versus displacement. This graph is a parabolic curve that opens upwards, with the minimum point representing the equilibrium position. The potential energy of the system is at its maximum when the displacement is at its maximum, and at its minimum when the displacement is at its equilibrium position.