Determining the Position as a Function of Time Equation

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In simple harmonic motion, the Position as a Function of Time Equation is expressed as x(t) = Acos(wt + phi). The choice between using "cos" or "sin" depends on the initial position of the system; "cos" is used when starting at the maximum displacement, while "sin" is appropriate when starting at the equilibrium position (0). Additionally, the phase angle phi can be adjusted for convenience, making it easier to work with aesthetically pleasing values. Ultimately, the decision may also depend on specific system characteristics that influence the setup. Understanding these nuances aids in accurately modeling harmonic motion.
jmason52
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In simple harmonic motion of a spring, the Position as a Function of Time Equation is: x(t) = Acos(wt+phi). How does one determine whether to use "cos" or "sin" when setting up the basic equation from the data given in a problem? Is it as simple as: use "sin" when x starts at equilibrium position (0), otherwise use "cos"? Can one of you offer me a simple clarification? Thanks!
 
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I believe it has to do with where it starts as you say. If it starts at the maximum point , you use cosine, if at 0 then sine.
 
You might consider using whichever makes the phase angle phi a nice value (magnitude, sign). Basically it's a matter of aesthetics unless some other part of the system under analysis forces your hand.
 

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