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Oscillation of a mass connected to a spring displaced

  1. May 3, 2015 #1
    1. The problem statement, all variables and given/known data

    A mass m hangs on a spring of constant k. In the position of static equilibrium the length of the spring is l. If the mass is drawn sideways and then released,the ensuing motion will be a combination of (a) pendulum swings and (b) extension and compression of the spring. Without using a lot of mathematics, consider the behavior of this arrangement as a coupled system.

    I have attached the figure I drew for this problem.

    2. Relevant equations

    3. The attempt at a solution

    For x - direction:

    ## m \cfrac{d^2 x}{d t^2} + m {\omega_{0}}^2 x = 0 ##
    ##\implies \cfrac{d^2 x}{d t^2} + {\omega_{0}}^2 x = 0 \tag{1} ##
    ##\implies \cfrac{d^2 x}{dt^2} + \cfrac{g}{l} x = 0\tag{1}##

    For y - direction:

    ## m \cfrac {d^2 y}{d t^2} + ky = mg ##
    ##\implies \cfrac{d^2 y}{d t^2} + \cfrac{k}{m} y = g \tag{2}##


    Solution for equation (1) would be:

    ## x = A \cos (\omega_{0} t) \tag{3}##

    Solution for equation (2) would be:

    ##y = B \cos (\omega t) \tag{4}##

    Am I on the right track and how should I proceed?

    Thanks
     

    Attached Files:

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    Last edited: May 3, 2015
  2. jcsd
  3. May 3, 2015 #2
    I'm not sure what constitutes "a lot of mathematics". It sounds to me like the questioner just wants you to (maybe) mathematically express some of the initial conditions, and then offer a qualitative explanation of the overall behavior of the system.

    I would advise you to wait to see someone else's take on the question, though.
     
  4. May 3, 2015 #3
    Thanks for the reply. I will wait for some other responses.
     
  5. May 4, 2015 #4

    BvU

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    Well, the problem statement in itself is already a bit strange to me: isn't there anything they want from you, other than that you 'consider' the system?

    And your equations seem a bit strange to me. Do you mean to say that the spring doesn't exercise any force in the x-direction ?
     
  6. May 4, 2015 #5
    Thanks for the reply. I am also stuck with what the question expects me to do. As for the force in x-direction, can you please tell me which other force will act ?
     
  7. May 4, 2015 #6

    BvU

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    Wall, what if the spring is at ana ngle ##\theta## wrt the vertical when it has a length ##l + \Delta l## ?
     
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