Deriving position function for object in SHM

  • Thread starter Callumnc1
  • Start date
  • #1
Callumnc1
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Homework Statement:
Please see the image below
Relevant Equations:
x(t) = Acos(wt + ϕ)
For this problem,
1670306945988.png

1670306964083.png

How did they get that formula shown?

My working is,
1670307096649.png

1670307174104.png

1670307305108.png


All the solutions wrote was,
1670307369422.png


Many thanks!
 

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Answers and Replies

  • #2
haruspex
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Your working headed off into a blind alley. You know that you need to be eliminating A, so tucking it inside an arccos function isn’t going to get you there.
Start by writing all three initial state equations: position, velocity and acceleration. Then see how you can combine them to eliminate one of the unknowns.
 
  • #3
Orodruin
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Please type out your work instead of attaching pictures. The pictures make it impossible to quote particular sections.

Edit: I suggest you change your unknowns from A and phi to something more direct.
 
  • #4
Callumnc1
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Your working headed off into a blind alley. You know that you need to be eliminating A, so tucking it inside an arccos function isn’t going to get you there.
Start by writing all three initial state equations: position, velocity and acceleration. Then see how you can combine them to eliminate one of the unknowns.
Thank you @haruspex and @Orodruin! I have solved the problem now.

Many thanks!
 
  • #5
haruspex
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Thank you @haruspex and @Orodruin! I have solved the problem now.

Many thanks!
You are welcome. But did you understand my comment about heading off into a blind alley? Recognising which directions cannot lead anywhere is a useful skill to develop.
 
  • #6
Callumnc1
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You are welcome. But did you understand my comment about heading off into a blind alley? Recognising which directions cannot lead anywhere is a useful skill to develop.
Thanks @haruspex! I did understand your comment, which I agree, would be very useful skill to have!

Many thanks,
Callum
 

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