Why are oscillatory motions sinusoidal in time?

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iurod
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Hi,
I having trouble grasping what: "oscillatory motions are sinusoidal in time" means... does this just mean that when solving a problem for simple harmonic motion that the equation is going to involve both and sin/cos and time? Sorry this might be more of a mathematical question.
 

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If you plot the position as a function of time, you'll get a sinusoidal graph. (Yes, descriptions of SHM will involve sines and cosines.)