Example 2.75. Determine the work that needs to be expended to compress an elastic spring by $\Delta h$ units of length. Perform the calculations assuming Hooke's law $F=-k x$ is valid.
Solution.

$$
A=\int_{0}^{\Delta h}(-k x) d x=-\left.k \frac{x^{2}}{2}\right|_{0} ^{\Delta h}=-\frac{k \Delta h^{2}}{2}
$$