Concept explainers
(a)
The time
(a)
Answer to Problem 19.16P
The time
Explanation of Solution
Given Information:
The cord length
At rest the angle
The distance (d) is 0.6 m.
Assuming the value of acceleration due to gravity (g) is
Calculation:
Calculate natural circular frequency for path
Substitute
The time period of oscillations corresponding to the natural circular frequency
Calculate the time period
Substitute
Calculate the length
Substitute 0.6 m for d.
Calculate the natural circular frequency
Substitute
The time period of oscillations corresponding to the natural circular frequency
Calculate the time period
Substitute
Calculate the time period to return to A using the relation:
Substitute 1.09876 s for
Therefore, the time
(b)
The amplitude
(b)
Answer to Problem 19.16P
The amplitude
Explanation of Solution
Given Information:
The cord length
At rest the angle
The distance (d) is 0.6 m.
Assume the acceleration due to gravity (g) is
Calculation:
For the path between the points A and B:
Consider point A:
The displacement at A
Consider point B:
Express the derivative of the displacement at B
Substitute
Express the velocity
Substitute Equation (1) for the value of
For the path between the points B and C:
Consider point C:
The displacement at C
Consider point B:
Express the derivative of the displacement at B:
Substitute
Express the velocity at B:
Substitute Equation (3) for the value of
Equate Equations (2) and (4).
Calculate the amplitude
Substitute 1.2 m for
Therefore, the amplitude
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Chapter 19 Solutions
VECTOR MECH. FOR EGR: STATS & DYNAM (LL
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