Difference between X and Amplitude (Simple Harmonic Motion)?

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SUMMARY

The discussion centers on the relationship between the equation for velocity in simple harmonic motion, V=Vo √(1-(x^2/a^2)), and the concept of amplitude. The user seeks to rearrange this equation to find the amplitude, which is defined as the maximum displacement of the spring. It is established that the speed of the object is zero at maximum displacement, leading to a straightforward solution for amplitude when substituting the maximum displacement into the velocity equation.

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V=Vo √1-(x^2/a^2)

X is the distance of the spring's stretch, but how would you rearrange the equation if you are looking for Amplitude? They both use the same units (meters) as far as I am concerned. Help would be appreciated, thanks; I am still a beginner with Physics.
 
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I'm guessing that this is the formula for the speed of the object attached to the spring as a function of the displacement ##x##. The amplitude is the maximum value of the displacement, so you should ask what the value of the speed is when the object is at the maximum displacement. That should lead to an easy to solve equation for the maximum displacement.
 

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