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Concept Problem: Pendulum

  1. Apr 9, 2013 #1
    The physical pendulum is an object suspended from some point a distance d from its center of mass. If its moment of inertia about the center of mass is given by:
    I= Icm + Md2
    where d is the distance from the pivot to the center of mass of the pendulum.

    Consider that some odd-shaped physical pendulum of mass M is suspended from some pivot point and displaced through a given angle θ, then released. If the pendulum has a moment of Intertia I about the pivot, then the differential equation describing its subsequent motion is
    Id2θ/dt2 = -Mgdsinθ

    a) Use the above info to justify that for a sufficiently small angular displacement, the physical pendulum oscillates with simple harmonic motion with angular frequency
    ω = √(mgd/I)

    SO: I know that I have to follow the argument for a simple pendulum to justify the solution for the physical pendulum. I think that is involves torque, angular acceleration, and/or moments of inertia. I am not sure how to fully justify the angular frequency equation.
     
  2. jcsd
  3. Apr 9, 2013 #2

    rude man

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    What is the differential equation you know for a simple pendulum?
     
  4. Apr 10, 2013 #3
    I'm confused if this is an actual question or one that is supposed to make me think.

    The differential equation for the motion of a pendulum is Id2θ/dt2
     
  5. Apr 10, 2013 #4

    haruspex

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    The DE above is not SHM. Your first step is to turn it into a DE for SHM by doing an approximation that's valid for small θ. Do you know a suitable approximation?
     
  6. Apr 10, 2013 #5

    rude man

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    The latter.

    That is not an equation. Where's the rest of it?
     
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