Finding the phase constant when initial displacement is zero and velocity is negative

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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.
 
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.
 
Have a gander:

Diagram of a mass on a vertical spring at equilibrium with an initial velocity arrow pointing down, beside two graphs of cos(ωt) and cos(ωt + φ) versus t, the second shifted by phase angle φ.
 
Attachments
  • Diagram of a mass on a spring at equilibrium, with graphs of y against t for cos(ωt) and cos(ωt + φ), showing the curve shifted by phase φ.
    Fig2.jpg
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