How to determine phase constant?

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SUMMARY

The discussion focuses on determining the phase constant of a mass-spring system oscillating at a frequency of 4.00 Hz. The mass of 225g is initially at a position of 5.00 cm with a velocity of -37.0 cm/s. The correct phase constant is calculated using the equations for velocity and position in simple harmonic motion (SHM), leading to a final phase constant of approximately 0.2893 radians. Participants clarified the use of both position and velocity to accurately determine the phase constant and discussed the correct formula for position at a given time.

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Homework Statement



A 225g mass attached to a horizontal spring oscillates at a frequency of 4.00 Hz. At t=0s, the mass is at x = 5.00 cm and has v_x = -37.0cm/s . Determine the phase constant.

Homework Equations



velocity = v(t)
v(t) = Aω·cos( ωt + ϕ )

The Attempt at a Solution



-37 cm/s = ( 5.2122*10^-2 m )( 25.133 rad/sec )cos( 0 + ϕ )
-0.282 = cos( ϕ )
ϕ = cos⁻¹( -0.282 )
ϕ = 106.40º = 1.857 radians ◄---

However that answer is wrong, and I am not sure why. Can anyone help?
 
Last edited:
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The result is correct, but you could have used both x(0) and v(0) to calculate the tangent of the phase constant, and decide about the quadrant by examining the sign of the sign and cosine.
It is possible that the SHM was defined as x(t)=cos(ωt + ϕ). Try it. ehild
 
Last edited:
So instead of using -37 use 5 instead? I tried that and got 1.5324 radians and it's still wrong, lmao. Hmm..
 
Last edited:
How did you get 1.5324 radians?

If x=Acos(ωt+φ), v=-Aωsin(ωt+φ), X(0)=5=Acosφ, v(0)=-37=-Aωsinφ:

tanφ=7.4/(8π)...

Both sine and cosine are positive so the angle is in the first quadrant.

ehild
 
Ah, thanks I see where I made the error. It was .2863rad. Thanks a lot!
 
Actually now I am having trouble with the last part, lol. The question is to determine the position at t = 5.00s .

I did this:

Position = s(t)
= A·sin[ ωt + ϕ ]
= ( .052122 m )sin[ (25.133 s⁻¹)( 5.0 s ) + .2893 ]

And got .01478 m, but that is wrong. Any help?
 
But we have figured out that the position was x=Acos( ωt + ϕ) with ϕ=0.2893...


ehild
 
ehild said:
But we have figured out that the position was x=Acos( ωt + ϕ) with ϕ=0.2893...


ehild

Wow, I didn't even realize, hah. Thanks again for all the help!
 

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