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Homework Help: Body suspended from a linear spring

  1. Sep 30, 2008 #1
    1. The problem statement, all variables and given/known data

    When a body is suspended from a fixed point by a certain linear spring, the angular frequency of the vertical oscillations is found to be [tex]\Omega[/tex]1. When a different linear spring is used, the oscillations have angular frequency . [tex]\Omega[/tex]2. Find the angular frequency of vertical oscillations when two springs are used together in parallel.

    Here is a link to the problem that provides hints to the problem: http://courses.ncsu.edu/py411/lec/001/: [Broken] Go to the Homework section of the webpage, then go to assignment 5, then go to problem 5.2.

    2. Relevant equations

    F=k*eff*[tex]\Delta[/tex] x
    [tex]\sqrt{k*eff/m}[/tex]=[tex]\Omega[/tex]



    3. The attempt at a solution

    The hint to the problem says I need to calculate restoring force for each cases.

    For the parallel case, would each of the two springs exert a contact force on each other since both bodies would be attached to two different springs?

    For the series case, both bodies would be in line with each other; would body would behind or in front of the other body, while sharing an attached spring; therefore I know that there is definetely

    [tex]\sqrt{k*(1)/(m)}[/tex]=[tex]\Omega[/tex]1 ==>

    [tex]\Omega[/tex]1^2=[tex]k*1/m}[/tex]
    [tex]\Omega[/tex]2^2=[tex]k*2/m}[/tex]

    F1= ([tex]\Omega[/tex]1^2)*m*[tex]\Delta[/tex] x
    F2= ([tex]\Omega[/tex]2^2)*m*([tex]\Delta[/tex] x)

    Not sure what my next step should be after that
     
    Last edited by a moderator: May 3, 2017
  2. jcsd
  3. Sep 30, 2008 #2
    anyone have a hard time reading my post?
     
  4. Sep 30, 2008 #3

    gabbagabbahey

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    Homework Helper
    Gold Member

    If the springs are attached in parallel, then the total restoring force is just [itex]F=F_1+F_2=k_{eff}\Delta x[/tex]. So what does that make [itex]k_{eff}[/itex]? How about [itex]\Omega_{eff}[/itex]?

    P.S. subscripts and superscripts in LaTeX are just A_{whatever} and A^{whatever}
     
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