**Potential Energy of a Spring Formula**

If the usual position(i.e., when not stretched), there is no energy in the spring. But, when the position is altered from its usual position, the spring is able to store energy by the virtue of its position. This stored energy is known as potential energy. Potential energy of the spring is the potential energy stored as a result of deformation of a particular elastic object, or a spring. It describes the work done to stretch the spring and depends on the spring constant k and the distance stretched.

The Potential energy of a spring is given by,

**P.E = ½ k x**^{2}

Where,

k = spring constant

x = spring displacement

**Example 1: **Determine the potential energy of a string whose spring constant is 200N/m and the displacement is 0.8m.

**Solution:**

Given parameters are,

k = 200N/m,

x = 0.8m

Potential energy of a string formula is given by,

P.E = 1 / 2 k x2

P.E = ½ 200 x (0.8)2

= 64 J

**Example 2: ****The **spring constant and displacement of a stretched string is 100N/m and 0.5m respectively. Determine the potential energy stored in the stretched string.

**Solution:**

Given parameters are,

k = 100N/m,

x = 0.5m

Potential energy of a string formula is given by,

P.E = 1 / 2 kx2

= 1 / 2 x 100 x (0.5)2

= 12.5 J