SHM question help pls asap

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Htx_x346
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#1
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How did they go from there to there in one step? How did they know not to use the cos function if that makes sense?Name:  1D2FD6A8-CB51-4F79-A819-9F3A11334660.jpeg
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mqb2766
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The cos() and sin() curves are related by a shift of pi/2, so if you set alpha appropriately, theyre the same, so either is fine.
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Htx_x346
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(Original post by mqb2766)
The cos() and sin() curves are related by a shift of pi/2, so if you set alpha appropriately, theyre the same, so either is fine.
Okay so i wont loose mark if i did Rsin(wt)?
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mqb2766
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(Original post by Htx_x346)
Okay so i wont loose mark if i did Rsin(wt)?
It would depend on the initial conditions. The shift of alpha means you can vary location of the sinusoidal solution, independent of whether you write
Rcos(wt+alpha)
or
Rsin(wt+alpha)
If you said the solution was Rsin(wt) then that would assume the displacement at time 0 was 0, so the "point" would be passing through the equilibrium position with a positive velocity.
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Htx_x346
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(Original post by mqb2766)
It would depend on the initial conditions. The shift of alpha means you can vary location of the sinusoidal solution, independent of whether you write
Rcos(wt+alpha)
or
Rsin(wt+alpha)
If you said the solution was Rsin(wt) then that would assume the displacement at time 0 was 0, so the "point" would be passing through the equilibrium position with a positive velocity.
Wdum by the intial conditions?
In an exam how would i know whether to re-write it as a function of sin or a function of cos?
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mqb2766
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(Original post by Htx_x346)
Wdum by the intial conditions?
In an exam how would i know whether to re-write it as a function of sin or a function of cos?
You can write either
Rcos(wt+alpha)
Rsin(wt+alpha)
Theyre equivalent (subject to alpha being set appropriately).

The original solution was
Acos(wt) + Bsin(wt)
Here you have two constants A and B which are determined by the value of the displacement and velocity at time 0 (usually). You have a second order differential equation, you need two initial conditions (x(0)=..., x'(0)=...) to get a particular solution where the values of A and B are determined. The above representations are equivalent, but the two constants to determine are R and alpha.

This must be covered in your textbook in this section?
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Htx_x346
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(Original post by mqb2766)
You can write either
Rcos(wt+alpha)
Rsin(wt+alpha)
Theyre equivalent (subject to alpha being set appropriately).

The original solution was
Acos(wt) + Bsin(wt)
Here you have two constants A and B which are determined by the value of the displacement and velocity at time 0 (usually). You have a second order differential equation, you need two initial conditions (x(0)=..., x'(0)=...) to get a particular solution where the values of A and B are determined. The above representations are equivalent, but the two constants to determine are R and alpha.

This must be covered in your textbook in this section?
I dont think its covered in my textbook
Yeah i just came across another example and here they use cos instead!
So how do i know whether to use cos or sin, sorry im still slightly confused.
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Htx_x346
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mqb2766
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(Original post by Htx_x346)
I dont think its covered in my textbook
Yeah i just came across another example and here they use cos instead!
So how do i know whether to use cos or sin, sorry im still slightly confused.
I can guarantee that just about all of this will be covered in your textbook.

Third time, theyre equivalent, you can use either. However
Rcos(wt+alpha)
is probably more common as the intiial coditions are usually that initially the velocity is 0 and the particle has a maximum displacement. This is what a basic cos() curve represents.
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mqb2766
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(Original post by Htx_x346)
How did they go from there to there in one step? How did they know not to use the cos function if that makes sense?Name:  1D2FD6A8-CB51-4F79-A819-9F3A11334660.jpeg
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As per the previous posts, the representations are equivalent. Its just the harmonic identities
https://www.examsolutions.net/tutori...ic-identities/
or whatever your textbook calls them.
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Htx_x346
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(Original post by mqb2766)
I can guarantee that just about all of this will be covered in your textbook.

Third time, theyre equivalent, you can use either. However
Rcos(wt+alpha)
is probably more common as the intiial coditions are usually that initially the velocity is 0 and the particle has a maximum displacement. This is what a basic cos() curve represents.
okay thanks, sorry was just making sure because i have an exam today.
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mqb2766
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(Original post by Htx_x346)
okay thanks, sorry was just making sure because i have an exam today.
Good luck, but if youre unsure about these worked examples it may be worth working through a similar question independently to make sure you do actually understand this.
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