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    Need any good physicists/mathematicians to give me a hand here...

    (i) What is the general solution to d^2y/dx^2 + 2k dy/dx + x = 0 when 0 < k < 1?

    This bit I can do, I get y = e^-k (A cos(1-k^2)^(1/2) x + B sin(1-k^2)^(1/2) x).

    (ii) We know that the above differential equation represents damped simpleharmonic motion with dampening factor k. Also we are given that x(0) = 0 (from this I deduced A = 0).

    Let x1, x2, x3 .... xn be the successive turning points such that if xn is a maximum, xn+1 is the following minimum.

    Show that the ratio |x(n+1) / xn| takes a value a, independent of n, and furthermore that we can show that k^2 = (ln a)^2/(pi^2 + (ln a)^2), where a is independent.

    For this last bit I've completely stuffed, I don't do A-Level physics, and havn't done M4 yet, which has damped SHM in, so I don't really know how to start....

    (Original post by theone)
    Need any good physicists/mathematicians to give me a hand here...

    (i) What is the general solution to d^2y/dx^2 + 2k dy/dx + x = 0 when 0 < k < 1?

    This bit I can do, I get y = e^-k (A cos(1-k^2)^(1/2) x + B sin(1-k^2)^(1/2) x).

    (ii) We know that the above differential equation represents damped simpleharmonic motion with dampening factor k. Also we are given that x(0) = 0 (from this I deduced A = 0).

    Let x1, x2, x3 .... xn be the successive turning points such that if xn is a maximum, xn+1 is the following minimum.

    Show that the ratio |x(n+1) / xn| takes a value a, independent of n, and furthermore that we can show that k^2 = (ln a)^2/(pi^2 + (ln a)^2), where a is independent.

    For this last bit I've completely stuffed, I don't do A-Level physics, and havn't done M4 yet, which has damped SHM in, so I don't really know how to start....
    where did you get this question if you don't do physics or P4?
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    (Original post by Unreg)
    where did you get this question if you don't do physics or P4?
    I do F Maths, and this is a STEP III Pure maths question...

    I would start by finding dy/dx = 0 to find where the turning points are.
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    (Original post by Unreg)
    I would start by finding dy/dx = 0 to find where the turning points are.
    But from what I've done it doesn't get anywhere.
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    Sorry to bump this but I need a hand

    (Original post by theone)
    Sorry to bump this but I need a hand
    If i had a pen and paper i would help you. plus im going in 5 minutes to the cinema for you-know-what.
 
 
 
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