What are the energy changes in simple harmonic motion?

The energy changes in simple harmonic motion involve the interconversion of kinetic and potential energy.

Simple harmonic motion is a type of periodic motion where the restoring force is directly proportional to the displacement from equilibrium. The motion of a mass-spring system is an example of simple harmonic motion. As the mass oscillates back and forth, the energy changes between kinetic and potential energy.

At the equilibrium position, the mass has zero potential energy and maximum kinetic energy. As the mass moves away from equilibrium, the potential energy increases and the kinetic energy decreases. At the maximum displacement, the mass has maximum potential energy and zero kinetic energy. As the mass moves back towards equilibrium, the potential energy decreases and the kinetic energy increases.

The total mechanical energy of the system remains constant throughout the motion, as long as there is no external force acting on the system. This is known as the conservation of energy. The total mechanical energy is the sum of the kinetic energy and potential energy:

E = K + U

where E is the total mechanical energy, K is the kinetic energy, and U is the potential energy.

The kinetic energy of the mass-spring system is given by:

K = (1/2)mv^2

where m is the mass of the object and v is the velocity.

The potential energy of the mass-spring system is given by:

U = (1/2)kx^2

where k is the spring constant and x is the displacement from equilibrium.

Therefore, the energy changes in simple harmonic motion involve the interconversion of kinetic and potential energy, with the total mechanical energy remaining constant.