The kinetic energy of the pom-pom came from potential energy in the system. How did potential energy gets stored in the spring/pom-pom system?

The elastic potential energy of a spring is the energy stored in the spring due to its elastic nature.

The potential energy stored in a spring is known as elastic potential energy. The elastic potential energy of a spring is the energy stored in the spring due to its elastic nature.

For example, when a spring is compressed it acquires potential energy which will be converted to kinetic energy of the object impacted by the spring.

The elastic potential energy of spring is given as;

where;

Thus, we can conclude that, the elastic potential energy of a spring is the energy stored in the spring due to its elastic nature.

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I believe that the answer is that in physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors. Common types of potential energy include the gravitational potential energy of an object that depends on its mass and its distance from the center of mass of another object, the elastic potential energy of an extended spring, and the electric potential energy of an electric charge in an electric field.

scientific laws are the result of testing theories and proving them to be facts.

the displacement produced by the body.  

the amount of force subjected to the body.  

the angle between the direction of force and displacement