How is energy conserved in simple harmonic motion?

Energy is conserved in simple harmonic motion due to the interplay between kinetic and potential energy.

In simple harmonic motion, the restoring force is proportional to the displacement from equilibrium, resulting in oscillation around a central point. As the object moves away from equilibrium, it gains potential energy, which is converted into kinetic energy as it moves towards equilibrium. At equilibrium, the potential energy is at a minimum and the kinetic energy is at a maximum.

As the object continues to oscillate, the potential and kinetic energies interchange, but the total energy remains constant. This is due to the conservation of energy, which states that energy cannot be created or destroyed, only transferred or converted from one form to another.

In a simple pendulum, for example, the potential energy is at a maximum when the pendulum is at its highest point, and the kinetic energy is at a maximum when the pendulum is at its lowest point. The total energy of the pendulum remains constant throughout its motion, as long as there is no external force acting on it.

Overall, the conservation of energy in simple harmonic motion is a fundamental principle that allows us to understand and analyse a wide range of physical phenomena, from oscillating springs to musical instruments.