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Period of Oscillations

  1. Oct 28, 2007 #1
    1. The problem statement, all variables and given/known data
    A solid, uniform disk of mass M and radius a may be rotated about any axis parallel to the disk axis, at variable distances from the center of the disk.

    If you use this disk as a pendulum bob, what is T(d), the period of the pendulum, if the axis is a distance d from the center of mass of the disk?

    I got the answer to be:

    T(d) =2{\pi}\sqrt{\frac{0.5a^{2}+d^{2}}{gd}}

    The period of the pendulum has an extremum (a local maximum or a local minimum) for some value of d between zero and infinity. Is it a local maximum or a local minimum?

    2. Relevant equations

    3. The attempt at a solution

    I graphed the function and saw that as d increases, the period T also increases to a maximum. However, I am not clear about the physical reason as to why this is so. Please advise.

  2. jcsd
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