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The period of the resulting SHM

  1. Dec 5, 2007 #1
    I need some serious help for finding the angular frequency of this system

    The 3.81 kg cube has edge lengths d = 5.40 cm and is mounted on an axle through its center. A spring (k = 1100 N/m) connects the cube's upper corner to a rigid wall. Initially the spring is at its rest length. If the cube is rotated 3.00° and released, what is the period of the resulting SHM?

    Here's a picture to help..

    http://farm3.static.flickr.com/2108/2077...

    solution:

    From the ref, the moment of inertia I of a rectangular prism is m*(a^2+b^2)/12; for a cube with side d, I = md^2/6. At a distance r from the center the effective mass I/r^2 = (m/6)*d^2/r^2; since d/r = sqrt(0.5) it's m/12. Then ω^2 = k/(m/12).
    Since 3 deg is a small angle we can ignore the variation of r with rotation.

    question:
    i m just confused where the 12 came from???
     
  2. jcsd
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