Figure below shows two pendulums suspended from frictionless pivots and connected at their midpoints by a spring. Assume that each pendulum can be represented by a mass M at the end of a massless bar of length L. Also assume that the displacement is small and linear approximations can be used for sin 0 and cos 0. The spring located in the middle of the bars is unstretched when 0, = 02. The input force is represented by f (t), which influences the left-hand bar only. Obtain the equations of motion and sketch a block diagram for them.

Figure below shows two pendulums suspended from frictionless pivots and connected at their midpoints by a spring. Assume that each pendulum can be represented by a mass M at the end of a massless bar of length L. Also assume that the displacement is small and linear approximations can be used for sin 0 and cos 0. The spring located in the middle of the bars is unstretched when 0, = 02. The input force is represented by f (t), which influences the left-hand bar only. Obtain the equations of motion and sketch a block diagram for them.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Free undamped vibrations

Whenever an object/system displaces in either side of its equilibrium position with the help of an external/internal means, then the object/system moves regularly or randomly on both sides of its equilibrium position. This motion is called vibration. Generally, there are three types of vibration: longitudinal vibration, transverse vibration, and torsional vibration.

Question

Figure below shows two pendulums suspended from frictionless pivots and connected at their
midpoints by a spring. Assume that each pendulum can be represented by a mass M at the end of a
massless bar of length L. Also assume that the displacement is small and linear approximations can be
used for sin 0 and cos 0. The spring located in the middle of the bars is unstretched when 0, = 02. The
input force is represented by f (t), which influences the left-hand bar only.
Obtain the equations of motion and sketch a block diagram for them.

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