## Elastic (potential) energy stored in the spring

The elastic energy is stored in the deformed spring.

Also called ‘potential energy,’ and denoted by E_{p}.

\[ Elastic \;energy \;E_p(J) = \frac{1}{2}kx^2 \]

m: Mass (kg)

k: Spring constant (N/m)

x: Deformation length of spring (m)

## The amount of work the spring has done to the object

The amount of work you do on an object is the product of the force applied to the object and its distance traveled.

When an object is moved by a spring, the elastic energy of the spring is equal to the amount of work that moves the object.

\[ \begin{align} Elastic \;energy &= Work \;done \;on \;an \;object \\ \frac{1}{2}kx^2 &= F \cdot s \end{align} \]