The elastic potential energy of an object is influenced by its spring constant, displacement, mass, and material properties.

Elastic potential energy refers to the energy stored in an object when it is either stretched or compressed. The amount of elastic potential energy stored is directly proportional to the square of its displacement from the equilibrium position. This relationship means that as an object is stretched or compressed further, the elastic potential energy increases significantly.

The spring constant, denoted as $k$, plays a crucial role in determining the elastic potential energy of an object. The spring constant is a measure of the stiffness of the spring, defined as the force required to stretch or compress the spring by a certain distance. A higher spring constant indicates a stiffer spring, which requires more force to achieve the same displacement, resulting in greater elastic potential energy stored in the spring.

Additionally, the mass of the object also impacts its elastic potential energy. A heavier object will necessitate a larger force to stretch or compress the spring, leading to an increase in the amount of elastic potential energy stored.

The material from which the object or spring is made also affects its elastic potential energy. Different materials exhibit varying spring constants, influencing the amount of force needed to stretch or compress the spring and, consequently, the elastic potential energy stored.

In conclusion, the elastic potential energy of an object is influenced by its spring constant $k$, displacement $x$, mass $m$, and the material properties. Understanding these factors is essential for comprehending the behavior of springs and other elastic materials.