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In Fig 15.19a, a meter stick swings about a pivot point at one end, at distance h from the stick's center of mass. What is the distance L_(0) between the pivot point O of the stick and the center of oscillation of the stick? |
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Answer» <P> Solution :Calculations: We want the LENGTH `L_(0)` of the simple pendulum (drawn in Fig 15.19b) that has the same period as the physical pendulum (the stick) of Fig 15.19a. Setting EQS. 15.44 and 15.47 equal yields.`T= 2pi sqrt((L_(0))/(g)) = 2pi sqrt((2L)/(3g))` You can see by inspection that `L_(v) = (2)/(3)L` `=((2)/(3)) (100cm) = 66.7cm` In Fig 15.19a point P marks this DISTANCE from suspension point O. Thus, point P is the stick.s center of oscillation for the given suspension point. Point P would be different for a different suspension choice.  (a) A meter stick suspended from one end as a physical pendulum. (b) A simple pendulum whose length `L_(0)` is chosen so that the periods of the two pendulums are equal. Point P on the pendulum of (a) marks the center of oscillation. |
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