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Unformatted text preview: The Simple Pendulum An application of Simple Harmonic Motion A mass m at the end of a massless rod of length L There is a restoring force which acts to restore the mass to θ =0 • Compare to the spring F s =kx • The pendulum does not display SHM m θ T mg θ sin mg F − = mgsin θ L But for very small θ (rad), we can make the approximation ( θ <0.5 rad or about 25°) → simple pendulum approximation L mg k kx F s L mg L s mg F L mg F s = ⇒ − = − = − = = = − = ⇒ ≈ ) ( r s since sin θ θ θ θ θ Arc length Looks like spring force Like the spring constant This is SHM Now, consider the angular frequency of the spring L g f L g m L mg m k π ω ω 2 1 / = = = = = Simple pendulum angular frequency Simple pendulum frequency • With this ω , the same equations expressing the displacement x , v , and a for the spring can be used for the simple pendulum, as long as θ is small • For θ large, the SHM equations (in terms of sin and cos) are no longer valid...
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This note was uploaded on 12/10/2011 for the course PHY 1111 taught by Professor Stencil during the Fall '11 term at UGA.
 Fall '11
 Stencil
 Force, Mass, Simple Harmonic Motion

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