Find the work that needs to be done to compress the spring by 20cm if, under the action of a force of 30N

Find the work that needs to be done to compress the spring by 20cm if, under the action of a force of 30N, the spring is compressed by 1cm.

Given:
F = 30 Newton;
dx = 1 centimeter = 0.01 meter – the amount by which the spring is compressed under the action of the force F;
dx2 = 20 centimeters = 0.2 meters.
It is required to determine A (Joule) – the work that must be done to compress the spring by the amount dx2.
Find the coefficient of elasticity of the spring:
k = F / dx = 30 / 0.01 = 30,000 Newtons / meter.
Perfect work of compressing the spring will go to increase its potential energy, that is:
A = E potential = k * dx ^ 2/2 = 30,000 * 0.2 ^ 2/2 = 15,000 * 0.2 ^ 2 = 0.04 * 15,000 = 600 Joules.
Answer: To compress the spring by 20 centimeters, you need to do a work equal to 600 Joules.