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M3 June 2013 Q6 part (b) Need Help! Watch

1. Hi guys

Need help with this question - I've linked the paper below for reference (question 6 is in page 10). It is basically two elastic springs stretched on a horizontal plane, with a particle attached in the middle. The particle is displaced from the equilibrium position, and part (b) asks to show that it moves with SHM.

Using the usual method, of F=ma, I resolved the forces, getting the value of acceleration=120-50x (refer to image attached below showing my working in black pen). This is not in the correct form to show SHM motion, so wrong answer.

I referred to the exam answer, which I have written out in the second image (red pen). The difference was that my 'x' was from point A, whereas the correct answer took the value of 'x' as the displacement from equilibrium position (OC).

I don't understand why both of them give a different answer, surely they should be the same? I hope I haven't just done an algebraic mistake either!

If someone could please show why my method is wrong, that would be much appreciated, or link me to a worked solution someone else has done.

https://8a40d6c38bafca75cc407741c0f3...%20Edexcel.pdf

My working in black, and exam answer in red:

Attachment 521947521949522000
[attach]5.219475219495219e+23[/attach]
Attached Images

2. (Original post by the_martian13)
.The difference was that my 'x' was from point A, whereas the correct answer took the value of 'x' as the displacement from equilibrium position (OC).
I am inclined to believe that this is your mistake. In order to prove SHM, you must consider displacement from the equilibrium position. Any other point will not work.
3. Right I see, that makes sense actually.

I assumed that the extended position value would be the same regardless of where you take the x value from, but it seems like the convention is that in order to be able to use/derive SHM properly you need to take the displacement/extension from the equilibrium position...
4. (Original post by the_martian13)
Right I see, that makes sense actually.

I assumed that the extended position value would be the same regardless of where you take the x value from, but it seems like the convention is that in order to be able to use/derive SHM properly you need to take the displacement/extension from the equilibrium position...
Yes - this is actually the definition of simple harmonic motion, where the restoring force is proportional to the displacement from the origin; which is why you must consider displacement from the equilibrium position.
5. That's great I think its cleared up my doubt now.

Thanks for the prompt help!
6. (Original post by the_martian13)
That's great I think its cleared up my doubt now.

Thanks for the prompt help!
No worries! Good luck with M3!

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