Oscillations: The position is modeled as x(t)=Acos(ωt+ϕ)

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Homework Help Overview

The discussion revolves around a problem related to oscillations, specifically analyzing the position of an object modeled by the equation x(t)=Acos(ωt+ϕ). Participants are tasked with determining the phase angle and the position of the object at a specific time, given its frequency and amplitude.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between the phase angle and the cosine function, questioning the assumptions made about the sign of the phase angle. There are attempts to calculate the phase angle using the given frequency and time values, with some participants suggesting to verify the results by substituting values back into the original equation.

Discussion Status

The discussion is active, with participants exploring different interpretations of the phase angle and its implications. Some guidance has been offered regarding the calculations, and there is a mix of proposed values for the phase angle, indicating ongoing exploration of the problem.

Contextual Notes

Participants are working under the constraints of the problem statement, which specifies the need for a positive phase angle between 0 and 2π. There is also a focus on ensuring that the calculations align with the conditions of the cosine function.

jdmaxwell02
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Homework Statement
A object oscillates with a frequency of 2.44 Hz. At t=0.246 s, the object is located at its amplitude A=+0.15 m.
The position is modeled as x(t)=Acos(ωt+ϕ)

Determine the phase angle (positive value between 0 and 2π):

a. Determine the phase angle (positive value between 0 and 2π):
b. Determine the position of the object at t=0 s.
Relevant Equations
w=2pi/T
What I have done so far:
Since x=A, cos(ωt+ϕ) must equal 1
cos-1(1)=0 so -ωt=ϕ
ω=2pi/(1/f)=15.3
ωt=3.7=ϕ
 
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jdmaxwell02 said:
Homework Statement:: A object oscillates with a frequency of 2.44 Hz. At t=0.246 s, the object is located at its amplitude A=+0.15 m.
The position is modeled as x(t)=Acos(ωt+ϕ)

Determine the phase angle (positive value between 0 and 2π):

a. Determine the phase angle (positive value between 0 and 2π):
b. Determine the position of the object at t=0 s.
Homework Equations:: w=2pi/T

What I have done so far:
Since x=A, cos(ωt+ϕ) must equal 1
cos-1(1)=0 so -ωt=ϕ
ω=2pi/(1/f)=15.3
ωt=3.7=ϕ

You have the equation ##\phi = -\omega t##, but you seem to have taken ##\phi## to be positive.
 
PeroK said:
You have the equation ##\phi = -\omega t##, but you seem to have taken ##\phi## to be positive.
So would ϕ be 3.77?
 
jdmaxwell02 said:
So would ϕ be 3.77?

Why not plug ##\omega, t## and ##\phi## into your equation and see whether you get ##\cos(\omega t + \phi) = 1##?
 
ϕ is 2.51 rad. Plugged it into my calculator. Thanks for the help!
 
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