Determining the Position as a Function of Time Equation

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SUMMARY

The Position as a Function of Time Equation for simple harmonic motion is defined as x(t) = Acos(wt + phi). The choice between using "cos" or "sin" depends on the initial conditions of the motion. If the object starts at the maximum displacement, "cos" is used; if it starts at the equilibrium position (0), "sin" is appropriate. The phase angle phi can also influence this decision, with the goal of achieving a simple and aesthetically pleasing representation.

PREREQUISITES
  • Understanding of simple harmonic motion principles
  • Familiarity with trigonometric functions (sine and cosine)
  • Knowledge of phase angles in wave equations
  • Basic calculus for interpreting motion equations
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  • Study the derivation of the Position as a Function of Time Equation in simple harmonic motion
  • Learn about phase angle adjustments in wave mechanics
  • Explore the impact of initial conditions on harmonic motion
  • Investigate applications of simple harmonic motion in real-world systems
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Students of physics, educators teaching mechanics, and anyone interested in understanding the principles of simple harmonic motion and its mathematical representations.

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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