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Axial, torsional and pendulum modes of vibration(harmonic motion)

  1. Sep 18, 2007 #1
    1. The problem statement, all variables and given/known data
    Hello,

    This is more of a conceptual question rather than a problem with numbers.
    I was wondering if anyone new if there is a relationship between axial, tortional and pendulum vibration. The context is a mass hanging off a spring.

    ie will the natural frequency of vibration be the same for all 3 types given the same mass and spring constant?








    2. Relevant equations






    3. The attempt at a solution

    I tried an experiment and my apparatus is simply a mass hanging off the end of a spring. The only materials i had were an old school stop watch and a ruler so i had alot of difficulty getting any measurements. none fo which were any real use

    i know that the natural frequency of axial vibration is

    w(n)= sqrt(k/m)

    where k= spring constant
    m= mass
    w(n)= natural frequency

    i worked out the spring constant by graphing different masses versus deflection.

    I also know the formula for frequency of a pendulum with a mass and a string, but not with a spring.

    my common sense tells me that the natural frequency for all three modes of vibration will be the same when using the same spring and mass but i have no proof to back this up.

    Ive searched the internet and havent found anything relevant.

    Any hints would be great.
     
  2. jcsd
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