Chapter 7: Problem 4
Consider the special case where the pendulum system of Problem \(7.3\) has the property that \(k / m \ll g / L\). If the pendulums are released from rest when in the configuration \(\theta_{1}(0)=\theta_{0}\) and \(\theta_{2}(0)=0\), show that the response is of the form $$ \begin{aligned} &\theta_{1}(t) \cong A_{1}(t) \cos \omega_{a} t=\theta_{0} \cos \omega_{b} t \cos \omega_{a} t \\ &\theta_{2}(t) \cong A_{2}(t) \sin \omega_{a} t=\theta_{0} \sin \omega_{b} t \sin \omega_{a} t \end{aligned} $$ $$ \omega_{a}=\left(\omega_{2}+\omega_{1}\right) / 2, \omega_{b}=\left(\omega_{2}-\omega_{1}\right) / 2 $$ where $$ \omega_{a}=\left(\omega_{2}+\omega_{1}\right) / 2, \quad \omega_{b}=\left(\omega_{2}-\omega_{1}\right) / 2 $$ Plot the response. What type of behavior does the pendulum system exhibit?
Short Answer
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Key Concepts
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