Simple Harmonic Motion - Conflicting equations

AI Thread Summary
The discussion centers on the equations for displacement in simple harmonic motion (SHM), highlighting a discrepancy between a textbook equation and a professor's notes. The textbook states x(t) = Acos(ωt + ɸ0), while the professor's notes provide y(x,t) = Asin(ωt - kx + ɸ0). The confusion arises from the additional term -kx in the second equation, which is used for sine waves propagating in a medium. For a specific problem involving a sine wave traveling to the left, the second equation is deemed appropriate with minor adjustments. Understanding when to use each equation is crucial for accurately describing wave motion.
jumbogala
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Homework Statement


What is the equation for the displacement of a sin wave (eg something in SHM)?

My book says x(t) = Acos(ωt + ɸ0)

My prof's notes say y(x,t) = Asin(ωt - kx + ɸ0)


Homework Equations





The Attempt at a Solution


I'm not confused about why one is sin and the other is cos. I'm confused why one has the extra term -kx. When do you use which?

I have a question that asks me to write the displacement for a sine wave traveling to the left with frequency 200 Hz, speed 400 m/s, amplitude 0.010 m, and initial phase 90 degrees. So I'm not sure which of the above to use.
 
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First one is the general equation of SHM.
The second one the equation of the sine wave propagating in a medium towards the positive x direction.
You have to use the second equation to find the displacement with a small modification.
 

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