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Engineering and Tech / System Dynamics 3 / Chapter 4 / Problem 4.54

System Dynamics | 3rd Edition | ISBN: 9780073398068 | Authors: William J Palm III

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Derive the equation of motion for the lever system shown

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QUESTION:

Derive the equation of motion for the lever system shown in Figure P4.54, with the force \(f\) as the input and the angle \(\theta\) as the output. The position \(\theta=0\) corresponds to the equilibrium position when \(f=0\). The lever has an inertia I about the pivot. Assume small displacements.

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QUESTION:

Derive the equation of motion for the lever system shown in Figure P4.54, with the force \(f\) as the input and the angle \(\theta\) as the output. The position \(\theta=0\) corresponds to the equilibrium position when \(f=0\). The lever has an inertia I about the pivot. Assume small displacements.

ANSWER:

Step 1 of 2

The following are given by the question:

At the equilibrium position,

The force,

The angle,

The moment of inertia equation,

Here, is the applied force to lever, is the moment of inertia, is the angular displacement, L is the total length, is the length of lever from the pivot, is the length between pivot and damper, is the length from pivot to bottom of the lever, is the damping constant and is the torsion spring constant.

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