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Find the magnitude of small oscillations

  1. May 17, 2007 #1
    1. The problem statement, all variables and given/known data


    a rope is tied between 2 walls as shown.a bead of mass 'm' is on the rope as shown. it is constrained to move in the horizontal direction. it is tied to a spring of force constant 'k'- N/m. the spring is initially at its free length 'H'. the bead is displaced by a small displacement 'x' in the horizontal direction. does it execute SHM.If so find the magnitude of small oscillations?
    no friction.


    the figure is attached!!






    2. Relevant equations
    T =2 pie/omega


    3. The attempt at a solution
    Consider the spring to make an angle q with the vertical
    The mass in equilibrium in the y direction at all the times
    Fsin q = mg
    F (h/l)=mg
    F = mgl/h
    -Fcosq = f_restoring
    -Fx/l = f_restoring
    -mgl/hl *x =f_restoring
    -mgx/h = f_restoring
    -mgx/h = ma
    ma+mgx.h = 0
    a differential equation
    omega = sqrt (g/h)
    T = 2 pie * sqrt (h/g)
    Now the answer is dimensionally correct

    method 2

    Since the force exerted by the spring is the vectorial sum of the forces along both the directions
    F_y/(F_x) = tan q
    -F_x= f_restoring = F_y/(tanq)
    F_y intially is mg
    f_restoring = -mgx/h
    so this would be give

    T= 2 pie *sqrt (h/g)

    An amazing result independent of the spring constant of the force
    A spring can only influence the motion along the direction of the spring

    Is the solution?? if yes can anybody explain what it means

    thank you
     

    Attached Files:

    • Shm.jpg
      Shm.jpg
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  2. jcsd
  3. May 17, 2007 #2
    Hello,

    I have a result which shows that the motion is NOT a simple harmonic moiton.
    Because the net force on the bead is proportional to [tex]x^3[/tex].
    This is just my opinion.


    Regards
     
  4. May 17, 2007 #3
    Can u please give your method
     
  5. May 17, 2007 #4

    Office_Shredder

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    This is the first sign something is wrong. Looking at your equations, I can't find anything that actually states the force the spring acts on the object (if it's there, it's certainly missing the spring constant
     
  6. May 17, 2007 #5
    Is the motion simple harmonic??Please help me
     
  7. May 17, 2007 #6

    Office_Shredder

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    I'll give you a hint

    Wrong! There's a spring pulling on it too
     
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