Simple Harmonic Motion- Phase Shift Help

[Brian M]

Homework Statement

A 590.0 g mass oscillates with an amplitude of 11.4 cm on a spring whose spring constant is 27.7 N/m. At t=0.00 s the mass is 3.14 cm to the right of the equilibrium position and moving to the right.

Homework Equations

x(t)=Acos(Wt + phi)

The Attempt at a Solution

I already found the angular frequency(W) to be 6.85 rad/s to give the equation

x(t)=0.114cos(6.85t + phi)

Then I plugged in the position and at t=o to give

0.0314=0.114cos(phi)

cos(phi)=(0.0314/0.114)

cos^-1= 1.29 rad

I took that number and added 3pi/2 to give a phase shift of 6.00 rad. Which is wrong, I'm not sure why that wouldn't be the correct answer. Thanks for the help.

 

[ehild]

cos(phi)=(0.0314/0.114)

cos^-1= 1.29 rad

I took that number and added 3pi/2 to give a phase shift of 6.00 rad.

Why did you add 3pi/2? cos(3pi/2+phi) is not 0.0314/0.114.

ehild

 

[Brian M]

My mistake, I left out a step. I thought the phase shift was greater than 1.29 rad, so i took the angle between that and 1/2pi (0.28 rad). I added that number to 3pi/2 for a phase shift of 4.99 rad, which is still wrong.

 

[ehild]

Draw the unit circle and see the cosine of which angles are equal.
Are not they phi and 2pi-phi?

ehild

 

[Brian M]

Yes they are, and 2pi-phi = 4.99 which I already tried. I'm stumped here

 

[ehild]

Have you tried really? If we take the direction "to the right" positive phi =4.991 or (-1.292) rad. No need to add anything.

ehild

 

[Brian M]

Yeah the correct answer was -1.29 rad. Thanks for the help