At what displacement P.E and K.E of a body executing SHM are equal
The potential energy (P.E) and kinetic energy (K.E) of a body executing simple harmonic motion (SHM) are equal at the endpoints of the motion, where the displacement is maximum. At these points, the body is farthest from the equilibrium position, and its velocity is zero. Therefore, all the energy of the system is in the form of potential energy. As the body moves towards the equilibrium position, the potential energy decreases and the kinetic energy increases, but at the endpoints, these energies are equal.
The potential energy (PE) and kinetic energy (KE) of a body executing Simple Harmonic Motion (SHM) are equal at the extreme points of its motion, where the displacement is maximum or minimum.
Let's consider a mass-spring system as an example of SHM. When the mass is at the extreme points of its motion, its displacement from the equilibrium position is maximum, either positive or negative. At these points, the potential energy is at its maximum value, and the kinetic energy is zero because the mass momentarily stops moving.
When the mass is at the equilibrium position, its displacement is zero. At this point, the potential energy is zero because there is no displacement from the equilibrium position. However, the kinetic energy is at its maximum value because the mass is moving with its maximum speed.
Therefore, the potential energy and kinetic energy of a body executing SHM are equal at the extreme points of its motion, where the displacement is maximum or minimum.