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Verifying two functions

  1. Oct 29, 2014 #1
    1. The problem statement, all variables and given/known data
    I am trying to solve the textbook questions, but the steps are not shown--any suggestions would be appreciated!:

    1) Verify that x(t) = Asin (wt) + B cos(wt), where w = (k/m)1/2 is a solution to Newton's equation for a harmonic oscillator.

    2) Verify that x(t) = Csin(wt + Φ) is a solution to Newton's equation for a harmonic oscillator.

    2. Relevant equations
    Given above...

    3. The attempt at a solution
    1) I only have a faint idea, but don't know where to progress.....

    2) I think I am going in a right direction, but don't know if it is of "ENOUGH" verification:

    sin(wt +Φ) = sin(wt)cosΦ + cos(wt)sinΦ, which I put into the x(t) function:
    x(t) = Csin(wt)cosΦ + Ccos(wt)sinΦ
    = c1sin(wt) + c2cos(wt)

    ∴ c1= CcosΦ
    c2= CsinΦ

    ...do I need further proof?
     
  2. jcsd
  3. Oct 30, 2014 #2

    BvU

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    1) The idea is that you fill in x(t) in "Newton's equation for a harmonic oscillator" . The equation is probably linear in x, so you can do the terms one by one and you can forget the constants A and B

    Same goes for 2). What you do in your attempt for 2) is convert a solution of type 2) into one of type 1. So once you've done 1) properly, you are also done with 2).

    You don't say, but I suppose in your context, Newton's equation for a harmonic oscillator is something like ##m\ddot x + k x = 0## ?
     
    Last edited: Oct 31, 2014
  4. Oct 30, 2014 #3

    haruspex

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    ... and that's the equation that should have been posted as "relevant equations".
     
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