Concept explainers
Period of small oscillation of rod.
Answer to Problem 19.71P
The period of small oscillation of rod is
Explanation of Solution
Given:
Weight of sphere A is
Weight of sphere B is
Concept used:
Draw the diagram for the system considers position 1 as datum.
Write the expression for height
Write the expression for height
Write the identity as
As the value of
Substitute
Write the expression for velocity of point C.
Here,
Write the expression for velocity of point A.
Here,
Write the expression for the conservation of energy.
Here,
The kinetic energy of the system at position one is zero as the system is in rest.
Write the expression for the potential energy at point (1).
Substitute
Here,
Write the expression for the kinetic energy at position (2).
Substitute
Here,
Potential energy at position (2) is zero.
Write the expression for the time period of oscillation.
Here,
Calculation:
Substitute
Substitute
Substitute
Simplify the above expression for
Substitute
The period of small oscillation of rod is
Conclusion:
Thus, the period of small oscillation of rod is
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Chapter 19 Solutions
Vector Mechanics for Engineers: Dynamics
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