Solution to the Simple Harmonic Motion Differential Equation
<p>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:</p>
<p><img alt="" src="https://miro.medium.com/v2/resize:fit:700/1*m1HXOAZO6-5FXtv5fi_Yuw.png" style="height:227px; width:700px" /></p>
<p>Note that this does indeed represent SHM if we recall the definition that SHM occurs when an object is subject to a force <em>proportional</em> and in the <em>opposite</em> 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:</p>
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