Example 2. How much work is required to stretch a spring by $0.06 m$, if a force of 1 N stretches it by 0.01 m?
Solution. According to Hooke's law, the force $X$ stretching the spring by $x \mu$ is $X=k x$, where $k$ is the proportionality coefficient. Assuming $x=0.01$ m and $X=1$ N, we get $k=100$, therefore, $X=k x=100 x$. The sought work is determined by the formula (5.24):

$$
A=\int_{0}^{0.06} 100 x d x=\left.50 x^{2}\right|_{0} ^{0.06}=0.18(\partial \varkappa)
$$