An object is undergoing simple harmonic motion

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Homework Help Overview

The discussion revolves around an object undergoing simple harmonic motion, characterized by a specified period and amplitude. The original poster seeks to determine the object's position relative to the equilibrium at a given time, having encountered a discrepancy between their calculated result and an expected answer.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the use of different trigonometric functions to model the motion, questioning the appropriateness of cosine versus sine based on initial conditions. There is also a focus on determining the phase shift and its implications for the calculations.

Discussion Status

Participants are actively engaging in clarifying the use of sine and cosine functions in the context of simple harmonic motion. Some guidance has been provided regarding the calculation of the phase shift, with suggestions to reconsider initial conditions and their impact on the chosen model.

Contextual Notes

There is an emphasis on understanding the derivation of formulas rather than relying solely on memorization. The original poster's confusion regarding the phase shift and initial conditions is noted, as well as the importance of accurately applying the mathematical model to the problem context.

Mdhiggenz
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Homework Statement


An object is undergoing simple harmonic motion with period 1.190 and amplitude 0.640

At t=0 the object is at x=0 . How far is the object from the equilibrium position at time 0.475 ?



Homework Equations





The Attempt at a Solution



x=Acos(ωt+∅)

x= 0.640cos(2∏/1.190*.475)=.639

The answer however is .379

What am I doing wrong?

Thank you

- higgenz
 
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Mdhiggenz said:
x=Acos(ωt+∅)

At t = 0, x = 0. What should the value of ∅ be?

You'd be better off modelling the motion as x = Asin(ωt)
 
Can you explain why you would use sin?
 
Mdhiggenz said:
Can you explain why you would use sin?

You're told that at t = 0, x = 0. Sketch the curves of x = Asin(ωt) and x = Acos(ωt) with t representing the horizontal axis and x, the vertical. Which of them passes through the origin (0,0)?

It's OK to use the phase-shifted cosine function x = Acos(ωt + ∅) as long as you calculate the value of the phase shift ∅. But you didn't.
 
I was a bit confused on how to calculate ∅

I know the formula for ∅ is arctan(-vox/ωxo)

But isn't the initial velocity zero which would make it ∅= to 0 ?
 
Mdhiggenz said:
I was a bit confused on how to calculate ∅

I know the formula for ∅ is arctan(-vox/ωxo)

But isn't the initial velocity zero which would make it ∅= to 0 ?

Don't get tied up in formulas you memorise. You must clearly understand the derivation of each formula you use, otherwise you'll use them in the wrong context.

Go back to what you wrote. x = Acos(ωt + ∅).

Now put t = 0 and x = 0 to get 0 = Acos(∅). So what should ∅ be?

Use this value of ∅ and try to rework your answer. You'll get a negative value, but it doesn't matter - they just want the numerical magnitude.
 
Excellent I got the answer than way as well. I appreciate you helping me out, and teaching me an alternative method!

Higgenz
 
Mdhiggenz said:
Excellent I got the answer than way as well. I appreciate you helping me out, and teaching me an alternative method!

Higgenz

You're welcome. :smile:
 

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