How can I find the value of phi in a simple harmonic motion equation?

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SUMMARY

The discussion focuses on determining the phase constant, φ, in the context of simple harmonic motion (SHM) equations. The correct velocity equation is identified as v = -Aωsin(ωt + φ), where A represents amplitude and ω is angular frequency. To find φ, users are advised to evaluate the displacement function at t=0 and analyze the corresponding graph. Understanding the relationship between the sine function and its maximum value is crucial for solving for φ.

PREREQUISITES
  • Understanding of simple harmonic motion principles
  • Familiarity with trigonometric functions, specifically sine
  • Knowledge of derivatives in calculus
  • Ability to analyze graphs of functions
NEXT STEPS
  • Study the derivation of the simple harmonic motion equations
  • Learn how to apply initial conditions to find phase constants in SHM
  • Explore the graphical representation of sine functions and their properties
  • Investigate the impact of phase shifts on waveforms in oscillatory motion
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and wave motion, as well as educators teaching simple harmonic motion concepts.

ice87
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http://noether.physics.ubc.ca/physics153/assign72k5.pdf

I don't get number 1 c, which equation do i use? and in general, how would I be able to find phi?

OK, i figured i should find the first derivative of the displacement formula, which becomes v = -Asin(wt + phi) but that still undoable, how do i find phi?
 
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Check your derivative. remember that max(sin(x)) is 1
 
ah yes, i see, it should be v = -A ωsin(ωt + φ), but that's just a typo, i actually had this equation when i wrote it down on paper. But i still don't know how to find phi
 
look at t=0 ... what's the function? what's the graph?
phi is just the "little wt offset" if you don't start the timer in synch.
 
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