Concept explainers
(a)
The period
(a)
Answer to Problem 19.51P
The period
Explanation of Solution
Given information:
A thin homogeneous wire is bent into the shape of an isosceles triangle of sides are b, b and 1.6b.
Calculation:
Show the position of centroid and distance as in Figure (1).
Write the equation for mass moment of inertia
Here, r is distance of each particle from the axis of rotation.
Calculate the expression for mass moment of inertia
Here,
Modify the above equation,
Calculate the centroid equation
Calculate the distance equation AG as below
Substitute
The external forces in the system are force due mass of the thin wire and the effective restoring couple is
Take moment about A in the system for external forces.
Substitute
Take moment about A in the system for effective forces.
Substitute
Equate the moment about A in the system for external and effective forces.
Compare the differential Equation (1) with the general differential equation of motion
Calculate the period of small oscillation
Substitute
Therefore, the period
(b)
The period
(b)
Answer to Problem 19.51P
The period
Explanation of Solution
Given information:
A thin homogeneous wire is bent into the shape of an isosceles triangle of sides are b, b and 1.6b.
Calculation:
Calculate the expression for mass moment of inertia
Substitute
Calculate the equation for distance GB by using the Pythagoras theorem:
Substitute
The external forces in the system are force due mass of the thin wire and the effective restoring couple is
Take moment about B in the system for external forces.
Substitute
Take moment about B in the system for effective forces.
Substitute
Equate the moment about B in the system for external and effective forces.
Compare the differential Equation (2) with the general differential equation of motion
Calculate the period of small oscillation
Substitute
Therefore, the period
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Chapter 19 Solutions
Connect 2 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics
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