Understanding the Phase Constant in Simple Harmonic Motion

[1MileCrash]

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.

 

[gneill]

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?

 

[1MileCrash]

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??

 

[gneill]

Does the mass start at a maximum extension like the cosine function does?

 

[1MileCrash]

No, initial displacement is 0. So, I need to find where cosx equals 0?

 

[gneill]

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.

 

[1MileCrash]

Still have no clue on this.

 

[gneill]

Have a gander: