Simple Harmonic Motion- Phase Shift Help

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Homework Help Overview

The discussion revolves around a problem in simple harmonic motion involving a mass-spring system. The original poster describes a scenario where a mass oscillates with a given amplitude and spring constant, and seeks assistance in determining the phase shift in the motion equation.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the calculation of the phase shift based on the cosine function and the implications of the angle derived from the position at time t=0. There is exploration of the relationship between angles on the unit circle and the correctness of the phase shift value.

Discussion Status

The discussion has progressed through various attempts to clarify the phase shift calculation. Some participants have provided guidance on interpreting the cosine function and its relation to the unit circle, while others have expressed confusion regarding the steps taken. A correct phase shift value has been identified, but the process leading to that conclusion remains under examination.

Contextual Notes

Participants are working within the constraints of homework rules, which may limit the information they can share or the methods they can use. There is an emphasis on understanding the underlying concepts rather than simply providing answers.

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

ehild
 
Yes they are, and 2pi-phi = 4.99 which I already tried. I'm stumped here
 
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
 
Yeah the correct answer was -1.29 rad. Thanks for the help
 

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