Two identical pendulums, each with mass (m) and length (l), are connected by a spring of stiffness

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Two identical pendulums, each with mass \(m\) and length \(l\), are connected by a spring of stiffness \(k\) at a distance \(d\) from the fixed end, as shown in Fig. 5.35.

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a. Derive the equations of motion of the two masses.

b. Find the natural frequencies and mode shapes of the system.

c. Find the free-vibration response of the system for the initial conditions \(\theta_{1}(0)=a\), \(\theta_{2}(0)=0, \dot{\theta}_{1}(0)=0\), and \(\dot{\theta}_{2}(0)=0\).

d. Determine the condition(s) under which the system exhibits a beating phenomenon.

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Mechanical Vibrations

ISBN: 9780134361925

6th Edition

Authors: Singiresu S Rao

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