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Normal modes-finding x1(t) & x2(t)

  1. Jun 28, 2017 #1
    1. The problem statement, all variables and given/known data

    https://1drv.ms/b/s!ApJAu5EMYb4JgpYy68UWlGVzp0PVLQ

    Problem 21

    upload_2017-6-28_8-10-40.png

    2. Relevant equations

    x1 = Aeiw0t + 3Be2iw0t
    x2 = 3Aeiw0t - Be2iw0t


    3. The attempt at a solution

    At t = 0 both masses at equilibrium so the above equations simplify to:

    0 = A + 3B
    0 = 3A - B

    Thus B = -2A. Is this wrong. Why? Here's the teacher answer: https://1drv.ms/b/s!ApJAu5EMYb4JgpYov43i3LZIO3MQhA

    Why does he only work with velocity equations & not the displacement ones?
     
    Last edited by a moderator: Jun 28, 2017
  2. jcsd
  3. Jun 28, 2017 #2
    Oh come on, this is ridiculous! Do you think it's acceptable to post a link to a document that takes 400 years to download, and just say "Problem 21" (out of 70!). Can't you be bothered to TYPE THE THING OUT? Have you read the "Guidelines for Students and Helpers"? After 40 posts you should be familiar with the etiquette. Do you expect anyone to make any effort for you if you make no effort for us?
     
  4. Jun 28, 2017 #3

    haruspex

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    According to the linked solution, your "relevant equations" are not quite right. x1 and x2 are only the real parts of the expressions on the right. If we also allow that A and B are complex constants then the algebra in your attempt at solution only concludes that their real parts are zero. To get info on the imaginary parts you need to plug in the boundary values for velocity.
     
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