Concept explainers
The period
Answer to Problem 19.87P
The period
Explanation of Solution
Given information:
The length of rod AB and CD is l.
The mass of the gear C is m.
The mass of the gear A is 4m.
The mass of rod AB
Assuming the acceleration due to gravity is g.
Calculation:
Show the position 1 and position 2 of the system with velocity as in Figure (1).
Write the kinematics relations of gear:
Let,
Substitute
For position 1:
Write the expression for centroidal mass moment of inertia gear C
Write the expression for centroidal mass moment of inertia of gear A
Write the expression for centroidal mass moment of inertia of rod AB
Write the expression for centroidal mass moment of inertia of rod CD
Write the expression the velocity of rod AB
Write the expression the velocity of rod CD
Write the expression for the kinetic energy
Substitute m for
Write the expression for the potential energy
For position 2:
Write the expression for the kinetic energy
Write the expression for the displacement
For small oscillation
Write the expression for the displacement
For small oscillation
Write the expression for the potential energy
Substitute
Express the term
Write the expression for the conservation of energy:
Substitute
Substitute
Calculate the period
Substitute
Therefore, the period
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Chapter 19 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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