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Coupled Oscillations Help - 2 masses, 3 springs (maths/physics) Watch

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    Can't work out how to derive the equations of motion, i get the forces -kx1 and -kx2 but i don't get the force from the middle spring, does it not depend on whether the spring is being stretched or compressed as to what direction it will be i.e x2 bigger than x1 or x1 bigger than x1.

    i also don't know how to draw a free body force diagram on the masses which i think will help.
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    See attached picture. I think I've got all of the signs right ...

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    (Original post by atsruser)
    See attached picture. I think I've got all of the signs right ...

    Name:  plane10007.jpg
Views: 65
Size:  350.1 KB
    you spoiled my fun ...

    I did not think there were many people here capable to do this and I was leaving this for tomorrow afternoon.

    (careful that the busybodies do not report you for giving solutions...)
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    (Original post by TeeEm)
    you spoiled my fun ...
    I'm sorry.

    I did not think there were many people here capable to do this and I was leaving this for tomorrow afternoon.
    I have my moments.

    (careful that the busybodies do not report you for giving solutions...)
    It's hard to answer such a question without drawing out all the vectors and doing it the whole thing. Anyway, the full solution is already there, and it's clearly the details of the signs that the OP wants.
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    (Original post by atsruser)
    I'm sorry.



    I have my moments.



    It's hard to answer such a question without drawing out all the vectors and doing it the whole thing. Anyway, the full solution is already there, and it's clearly the details of the signs that the OP wants.
    totally agree with your last point but I have been reported for that
    Usually these individuals help at the lower echelons so highly unlikely there will enter this thread

    all the best.
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    (Original post by atsruser)
    I'm sorry.

    I have my moments.

    It's hard to answer such a question without drawing out all the vectors and doing it the whole thing. Anyway, the full solution is already there, and it's clearly the details of the signs that the OP wants.
    (Original post by TeeEm)
    totally agree with your last point but I have been reported for that
    Usually these individual help at the lower echelons so highly unlikely there will enter this thread

    all the best.
    I don't see any problem here - this is about "understanding the gaps in the book's presentation", not "please do this exercise for me".

    Higher-level textbooks can be notorious for skipping steps that aren't immediately obvious sometimes
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    (Original post by davros)
    I don't see any problem here - this is about "understanding the gaps in the book's presentation", not "please do this exercise for me".

    Higher-level textbooks can be notorious for skipping steps that aren't immediately obvious sometimes
    As I said, I fully agree with both atsruser and you
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    (Original post by atsruser)
    See attached picture. I think I've got all of the signs right ...

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    i get everything except the extension in the second spring. why can it not be x1-x2?
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    are assuming the spring has been stretched overall and that x2 is bigger than x1?
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    (Original post by Jammy4410)
    are assuming the spring has been stretched overall and that x2 is bigger than x1?
    No. With the vectors as I drew them (in the +ve direction), you can see that if spring 3 is at natural length l:

    a) if m_1 doesn't move, then x_2 increases the length of spring 3 to l+x_2
    b) if m_2 doesn't move, then x_1 decreases the length of spring 3 to l-x_1

    so if both change, then the extension e_1 (the overall change in length) is x_2-x_1.

    You can then check other cases to convince yourself that the vectors add up correctly to give the correct cases of tension or compression in the spring.

    E.g. with +ve x_2,x_1

    a) if x_2 > x_1 \Rightarrow x_2 -x_1 > 0 then spring 3 is in tension.
    b) if x_2 < x_1 \Rightarrow x_2 -x_1 < 0 then spring 3 is in compression.

    Or:

    With -ve x_1, +ve x_2 then x_2-x_1 > x_2 >0 and spring 3 is in tension.

    and so on.
 
 
 
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