Concept explainers
(a)
The frequency
(a)
Answer to Problem 19.89P
The frequency
Explanation of Solution
Given information:
The mass
The mass
The length (l) of the bar is 0.7 m.
The spring constant (k) is
The value of a is 0.5 m.
Assume the acceleration due to gravity (g) as
Calculation:
Show the position 1 and position 2 of the system as in Figure (1).
For position 1(Maximum velocity):
Calculate the mass moment of inertia bar ABC
Substitute 1.5 kg for
Write the expression the maximum velocity of sphere
Write the expression the maximum velocity of rod ABC
Write the expression for the kinetic energy
Substitute 2 kg for
Write the expression for the potential energy
For position 2:
Write the expression for the kinetic energy
Write the expression for the displacement in sphere
For small oscillation
Write the expression for the displacement of rod ABC
For small oscillation
Write the expression for the displacement of spring
For small angle
Write the expression for the potential energy
Substitute
Substitute
Express the term
Write the expression for the conservation of energy
Substitute
Substitute
Substitute 0.5 m for a in Equation (1).
Calculate the frequency
Substitute
Therefore, the frequency
(b)
The smallest value of a for which oscillation will occur.
(b)
Answer to Problem 19.89P
The smallest value of a for which oscillation will occur is
Explanation of Solution
Given information:
The mass
The mass
The length (l) of the bar is 0.7 m.
The spring constant (k) is
The value of a is 0.5 m.
Assuming the acceleration due to gravity (g) as
Calculation:
Calculate the value of a:
Substitute 0 for
Therefore, the smallest value of a for which oscillation will occur is
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Chapter 19 Solutions
Vector Mechanics for Engineers: Statics and Dynamics