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Unformatted text preview: 1 Physics 1D03 1 SHM and Circular Motion The Physical Pendulum and other oscillators Serway 15.4, 15.5 Practice: chapter 15, problems 22, 23, 25, 29, 31, 47, 55 Physics 1D03 2 Simple pendulum: a particle on a massless string. P CM mg Physical pendulum: any rigid body, pivoted at P, and free to swing back and forth. To find the period: 1) Consider the torque due to gravity 2) Write ( ) = I = I (d 2 / dt 2 ) 3) SHM if is proportional to  2 Physics 1D03 3 Calculate torque about the end: =  = 2 3 1 2 sin ML L Mg I Example: a metre stick, pivoted at one end. What is its period of oscillation? Uniform thin rod, pivot at end: I = 1 / 3 ML 2 sin 2 3 2 2 L g dt d = = and so Note, this does not describe SHM! Mg L Physics 1D03 4 But for small oscillations, sin This is like a simple pendulum of length 2 / 3 L . L g 2 3 = g L T 3 2 2 2 = = 2 2 2 2 3 = L g dt d so The angular frequency is and the period is Mg L 3...
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 Fall '09
 MCKAY
 Physics, Circular Motion, Mass

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