How do you find the initial phase angle?

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Homework Help Overview

The problem involves a mass oscillating on a vertical spring in simple harmonic motion (SHM). The mass has an amplitude of 10.0 cm and a period of 0.500 s. At time t = 0, the mass is positioned at -7.50 cm relative to the equilibrium position. The task is to find the initial phase angle, φ, using the equation x(t) = A cos(ωt + φ).

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss setting x(0) = -7.5 cm to find φ, while questioning the necessity of calculating A and ω first. There is uncertainty about how to apply the equation correctly and what values need to be determined.

Discussion Status

The discussion is ongoing, with participants providing guidance on how to approach the problem. Some clarification on the application of the equation has been offered, but there is still confusion regarding the steps to take and the values needed for calculation.

Contextual Notes

Participants note the importance of determining the values for amplitude and angular frequency before solving for the phase angle, indicating that these values are essential for the equation's application.

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Homework Statement



A mass is hanging on a vertical spring, and oscillates in SHM with an amplitude of 10.0 cm, and period 0.500 s. The graph shows its motion as a function of time. At t = 0, the mass is found at x = -7.50 cm below the equilibrium position.

Assuming that x(t) = A cos (ωt + φ), find the value of the initial phase angle, φ.

Homework Equations





The Attempt at a Solution



How do I get started in finding the initial phase angle, φ?
 
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Set x(0) = -7.5 cm and solve for the angle. You know the A and the w, so only one unknown.
 
Delphi51 said:
Set x(0) = -7.5 cm and solve for the angle. You know the A and the w, so only one unknown.

Im sorry I don't quite understand. It has to be x(t) = A cos (ωt + φ)

So don't I have to figure out A, ω, and t ? then just solve for φ ?

How come you just put x(0) = -7.5cm ? (I understand why you put x(0))

Thanks very much for the help!
 
Sorry, I should have written x(0) = A cos(ω*0 + φ) = -7.5 cm.
You WILL have to calculate numbers for ω and A before you can solve for φ.
 

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