What are the energy transformations in a simple harmonic oscillator?

The energy transformations in a simple harmonic oscillator involve the conversion of potential energy to kinetic energy and vice versa.

In a simple harmonic oscillator, such as a mass-spring system, the energy transformations occur between potential energy and kinetic energy. When the mass is at its maximum displacement from equilibrium, it has maximum potential energy. As it moves towards equilibrium, the potential energy is converted into kinetic energy. At the equilibrium point, the mass has maximum kinetic energy and zero potential energy. As it moves away from equilibrium, the kinetic energy is converted back into potential energy.

The total energy of the system remains constant, as dictated by the principle of conservation of energy. This can be expressed mathematically as:

E = 1/2 kA^2

where E is the total energy of the system, k is the spring constant, and A is the amplitude of the oscillation.

The maximum potential energy and maximum kinetic energy can also be expressed mathematically as:

Ep = 1/2 kA^2

Ek = 1/2 mv^2

where Ep is the potential energy, Ek is the kinetic energy, m is the mass of the object, and v is its velocity.

Overall, the energy transformations in a simple harmonic oscillator involve the conversion of potential energy to kinetic energy and vice versa, with the total energy of the system remaining constant.