Discussion
Which of the following equations represents a simple harmonic motion? (x is displacement and a is acceleration)
Answer: B
Simple harmonic motion is represented by a = -10x.
SHM is defined by an acceleration proportional to the displacement and directed opposite to it: \(a = -\omega^{2}x\). Here \(\omega^{2} = 10\), so \(\omega = \sqrt{10}\) rad/s.
a = 1.2x is proportional but points away from equilibrium, so the motion runs away instead of oscillating. \(a = 0.9x^{2}\) and \(a = 100x^{3}\) are not proportional to x, and \(a^{2} = 12x\) is not even linear in a.
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