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

[jdmaxwell02]

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

 

[PeroK]

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.

 

[jdmaxwell02]

You have the equation $\phi = -\omega t$, but you seem to have taken $\phi$ to be positive.

So would ϕ be 3.77?

 

[PeroK]

So would ϕ be 3.77?

Why not plug $\omega, t$ and $\phi$ into your equation and see whether you get $\cos(\omega t + \phi) = 1$?

 

[jdmaxwell02]

ϕ is 2.51 rad. Plugged it into my calculator. Thanks for the help!