The equation of motion of a simple pendulum, subjected to a constant torque, (M_{t}=m l^{2} f), is

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The equation of motion of a simple pendulum, subjected to a constant torque, \(M_{t}=m l^{2} f\), is given by

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If \(\sin \theta\) is replaced by its two-term approximation, \(\theta-\left(\theta^{3} / 6\right)\), the equation of motion becomes

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Let the solution of the linearized equation

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be denoted as \(\theta_{1}(t)\), and the solution of the equation

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be denoted as \(\theta_{2}(t)\). Discuss the validity of the total solution. \(\theta(t)\), given by \(\theta(t)=\theta_{1}(t)+\theta_{2}(t)\), for Eq. (E.2).

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Mechanical Vibrations

ISBN: 9780134361925

6th Edition

Authors: Singiresu S Rao

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