Understanding the Phase Constant in Simple Harmonic Motion

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Homework Help Overview

The discussion revolves around determining the phase constant in the context of simple harmonic motion, specifically for a mass oscillating on a spring. The original poster presents a scenario where the initial displacement is zero and the initial velocity is directed negatively.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between the phase constant, initial displacement, and initial velocity. Questions arise regarding the characteristics of the cosine function and how they relate to the given initial conditions.

Discussion Status

Participants are actively engaging with the problem, sketching cosine curves, and questioning the implications of the initial conditions on the phase constant. There is a recognition of the need to find where the cosine function equals zero and the direction of motion, but clarity is still being sought.

Contextual Notes

There is an emphasis on understanding the initial conditions and their impact on the phase constant, with some confusion about the relationship between the cosine function and the physical scenario described.

1MileCrash
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Homework Statement



The displacement of a mass oscillating on a spring is given by x(t) = xmcos(ωt + ). If the initial displacement is zero and the initial velocity is in the negative x direction, then the phase constant is:

Homework Equations





The Attempt at a Solution



How do I start? The book just tells me that the phase constant depends on displacement and velocity when t = 0, but doesn't say how.
 
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Sketch a cosine curve. What's its initial value? Where on the curve would match the initial condition of the spring and mass? What's (angular) the offset from zero?
 
gneill said:
Sketch a cosine curve.

OK

What's its initial value?

1

Where on the curve would match the initial condition of the spring and mass?

Huh??
 
Does the mass start at a maximum extension like the cosine function does?
 
No, initial displacement is 0. So, I need to find where cosx equals 0?
 
1MileCrash said:
No, initial displacement is 0. So, I need to find where cosx equals 0?

Not only that, but where it's going through zero and going negative, just like the mass' displacement.
 
Still have no clue on this.
 
Have a gander:

attachment.php?attachmentid=40822&stc=1&d=1320887764.jpg
 

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