Question

0 ?? L g A m ?? L m f(t) B Figure 1: The double pendulum in a vertical plane.

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L
g
A
m
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L
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f(t)
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Figure 1: The double pendulum in a vertical plane.

Added by Amy C.

University Physics with Modern Physics

Hugh D. Young 14th Edition

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Solved by Expert Rashmi Prakash

Step 1

For the upper bob: - The weight force mg acts vertically downward. - The tension force T1 in the upper linkage arm acts towards the pivot point. - The centrifugal force m(Lθ1̇)²L acts radially outward. For the lower bob: - The weight force mg acts vertically Show more…

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A double pendulum consists of two bobs, each with a mass of m, that can move in a vertical plane. There is an external time-dependent force f(t) acting on the lower bob in the horizontal direction. The pendulum has two rigid linkage arms with a length of L and negligible mass. Theta1 and theta2 can be used as generalized coordinates. We will ignore any friction and damping effects. Question: Obtain the equations of motion for the two bobs in the double pendulum using Newton's Second Law, free-body diagrams, and rotational equations of motion. Figure 1: The double pendulum in a vertical plane.