Simple harmonic motion (SHM) is a relatively common aspect of classical mechanics and in this article I will be solving the following differential equation that illustrates SHM:
Note that this does indeed represent SHM if we recall the definition that SHM occurs when an object is subject to a force proportional and in the opposite direction of its displacement. Mathematically this can be represented as F = -kx where k is a constant and we assume our displacement is in the x-direction. Since F = ma, this can be rearranged as follows: