Concept explainers
(a)
The expression for the position of the particle as a function of time.
(a)
Answer to Problem 9P
The expression for the position of the particle as a function of time is
Explanation of Solution
Given information:
The amplitude of the motion of the particle is
The expression for the position of the particle for
The formula to calculate angular frequency is,
Substitute
For
Substitute
Conclusion:
Therefore, the expression for the position of the particle as a function of time is
(b)
The maximum speed of the particle.
(b)
Answer to Problem 9P
The maximum speed of the particle is
Explanation of Solution
Given information:
The amplitude of the motion of the particle is
The formula to calculate maximum velocity is,
Substitute
Conclusion:
Therefore, the maximum speed of the particle is
(c)
The earliest time at which the particle has
(c)
Answer to Problem 9P
The earliest time at which the particle has
Explanation of Solution
Given information:
The amplitude of the motion of the particle is
The expression for velocity is,
Substitute
Substitute
Conclusion:
Therefore, the earliest time at which the particle has
(d)
The maximum positive acceleration of the particle.
(d)
Answer to Problem 9P
The maximum positive acceleration of the particle is
Explanation of Solution
Given information:
The amplitude of the motion of the particle is
The expression for acceleration is,
Substitute
Conclusion:
Therefore, the maximum positive acceleration of the particle is
(e)
The earliest time at which the particle has
(e)
Answer to Problem 9P
The earliest time at which the particle has
Explanation of Solution
Given information:
The amplitude of the motion of the particle is
The expression for velocity is,
Substitute
Substitute
Conclusion:
Therefore, the earliest time at which the particle has
(f)
The total distance traveled by the particle between
(f)
Answer to Problem 9P
The total distance traveled by the particle between
Explanation of Solution
Section 1;
To determine: The time period of the particle.
Answer: The time period of the particle is
Given information:
The amplitude of the motion of the particle is
The time period of the particle is,
Substitute
Section 2;
To determine: The number of time period of the particle.
Answer: The number of time period of the particle is
Given information:
The amplitude of the motion of the particle is
The number of time periods is calculated as,
This number of the periods shows that it completes one and half cycle approximately.
Section 3;
To determine: The total distance traveled by the particle between
Answer: The total distance traveled by the particle between
Given information:
The amplitude of the motion of the particle is
For one and half cycle the total distance is given as,
Substitute
Conclusion:
Therefore, the total distance traveled by the particle between
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Chapter 12 Solutions
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