Position in Motion: When to Use Cos & Sin in x=A*sin(wt+phi) or x=A*cos(wt+phi)?

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SUMMARY

The discussion centers on the application of the equations x = A*sin(wt + phi) and x = A*cos(wt + phi) in modeling motion. The choice between sine and cosine depends on the initial conditions of the motion. If the object starts at x = 0 when t = 0, the sine function is preferable. Conversely, if the object begins at its maximum position (amplitude) at t = 0, the cosine function is more suitable. Both functions can be used interchangeably by adjusting the phase factor accordingly.

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  • Understanding of harmonic motion principles
  • Familiarity with trigonometric functions (sine and cosine)
  • Knowledge of phase shifts in wave equations
  • Basic grasp of initial conditions in physics
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Tricks67
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In what kind of cases do u we formulate the equation type x=Asin(wt+phi) or x=Acos(wt+phi)...and if for example we use it to define the position of some thing in motion when do we know when to use cos and when to use sin...?
 
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It doesn't really matter which you use. The only difference is what position on the wave corresponds to phi = 0. A sin(wt+phi + pi/2) = A cos(wt+phi)
 
Tricks67 said:
when do we know when to use cos and when to use sin...?

It depends on the initial conditions for your specific situation. If the object is at x = 0 when t = 0, then it's easiest to use a sine wave. If the object is at x = maximum (i.e. the amplitude) when t = 0 then it's easiest to use a cosine wave.

However, as AlephZero noted, you can use either kind of wave in any case, by including an appropriate phase factor.
 
and we find the phase factor by setting x=0, right?
 

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