Solving Equation of Motion for A and \Phi

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SUMMARY

The discussion focuses on solving the equation of motion represented by A sin(wt + Φ) = 0, where the objective is to determine the values of A and Φ. The equation can be expanded using the identity A sin(wt)cos(Φ) + A cos(wt)sin(Φ) = 0. Participants suggest using the magnitude to find A and substituting specific values to isolate Φ, particularly by evaluating the equation at t = 0. The discussion highlights the need for a systematic approach to derive both variables from the given equation.

PREREQUISITES
  • Understanding of trigonometric identities and their applications
  • Familiarity with the concepts of angular frequency and phase in harmonic motion
  • Basic knowledge of calculus, particularly differentiation
  • Ability to manipulate and solve algebraic equations
NEXT STEPS
  • Study the application of trigonometric identities in solving equations
  • Learn about the significance of amplitude (A) and phase (Φ) in wave motion
  • Explore techniques for solving differential equations in physics
  • Investigate the use of initial conditions to solve for unknowns in equations of motion
USEFUL FOR

Students of physics, particularly those studying mechanics and wave motion, as well as educators looking for methods to teach the concepts of amplitude and phase in harmonic functions.

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Homework Statement



A sin (wt + [tex]\Phi[/tex]) = 0
Find A and [tex]\Phi[/tex]

Homework Equations



Asin(wt)cos[tex]\Phi[/tex] + Acos(wt)sin[tex]\Phi[/tex] = 0

The Attempt at a Solution



I was told to use magnitude to figure out A and something else to find [tex]\Phi[/tex] in variable.
I absolutely have no idea what to do...
I found a part of solution, which got me w and I am expected to solve for A and [tex]\Phi[/tex] with that given equation.

I tried to use original equation by plugging in t = 0 for A sin (wt + [tex]\Phi[/tex]) and first and second derivative from original equation.

I think once I get those A and [tex]\Phi[/tex], I "might" be able to solve entire problem.

Thank you.
 
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