How do you calculate the potential energy in SHM?

The potential energy in Simple Harmonic Motion (SHM) is calculated using the formula PE = 1/2 kx².

In Simple Harmonic Motion (SHM), potential energy (PE) is the energy stored in the system due to its position or configuration. It is one of the two forms of energy in SHM, the other being kinetic energy. The potential energy in SHM is directly proportional to the square of the displacement from the equilibrium position (x), and is given by the formula PE = 1/2 kx², where k is the spring constant.

The spring constant (k) is a measure of the stiffness of the spring. It is defined as the force required to compress or extend the spring by unit length. The spring constant is always positive, as it takes a force to change the spring's length. The displacement (x) is the distance moved by the object from its equilibrium position. It can be positive or negative, depending on the direction of the displacement.

The potential energy is maximum at the extreme positions of the motion (i.e., when the displacement is maximum), and it is minimum (zero) at the equilibrium position. This is because the displacement from the equilibrium position is maximum at the extreme positions and zero at the equilibrium position. Therefore, the potential energy, being directly proportional to the square of the displacement, is maximum at the extreme positions and zero at the equilibrium position.

In SHM, the total energy of the system (the sum of the kinetic and potential energies) is conserved. This means that when the potential energy is maximum, the kinetic energy is minimum (zero), and vice versa. This is because the energy is continuously transferred between the kinetic and potential forms as the object oscillates.

In conclusion, the potential energy in SHM can be calculated using the formula PE = 1/2 kx². It is directly proportional to the square of the displacement from the equilibrium position, and varies between a maximum value at the extreme positions and a minimum value at the equilibrium position.