How is energy conserved in SHM?

Energy is conserved in Simple Harmonic Motion (SHM) by the continuous interchange between kinetic and potential energy.

In SHM, an object oscillates back and forth about a stable equilibrium position. The total energy of the system remains constant, but it is continuously transferred between kinetic energy (the energy of motion) and potential energy (the energy stored due to position or configuration). This is the principle of conservation of energy, a fundamental concept in physics.

Let's consider a simple pendulum, a classic example of SHM. When the pendulum is at its maximum displacement (furthest point from the equilibrium), it momentarily comes to rest before changing direction. At this point, all the energy in the system is potential energy, as the pendulum is at its highest point. As the pendulum swings back towards the equilibrium position, this potential energy is gradually converted into kinetic energy. At the equilibrium position, the pendulum is moving at its fastest, so all the energy is kinetic. As the pendulum continues to swing to the other side, this kinetic energy is converted back into potential energy. This cycle repeats as long as no external forces (like friction or air resistance) are acting on the system.

The same principle applies to other examples of SHM, such as a mass on a spring. When the spring is stretched or compressed to its maximum extent, the system has maximum potential energy and zero kinetic energy. As the mass moves towards the equilibrium position, the potential energy decreases while the kinetic energy increases. At the equilibrium position, the kinetic energy is at a maximum and the potential energy is zero. As the mass moves past the equilibrium position, the kinetic energy decreases while the potential energy increases.

In an ideal SHM system, this energy transfer between kinetic and potential energy continues indefinitely, with no energy lost to the surroundings. However, in real-world systems, some energy is usually lost due to factors like friction or air resistance. Despite these losses, the principle of conservation of energy still applies: the total energy in the system (including any energy lost to the surroundings) remains constant.