
Concept explainers
(a)
The position of the particle at the end of
(a)

Answer to Problem 11P
The position of the particle at the end of
Explanation of Solution
Given information:
The initial position of the particle is
The formula for the position of the particle is,
Substitute
Conclusion:
Therefore, the position of the particle at the end of
(b)
The velocity of the particle at the end of
(b)

Answer to Problem 11P
The velocity of the particle at the end of
Explanation of Solution
Given information:
The position of the particle is
The formula for the velocity of the particle is,
Substitute
Conclusion:
Therefore, the velocity of the particle at the end of
(c)
The position of the particle in
(c)

Answer to Problem 11P
The position of the particle in simple harmonic motion for
Explanation of Solution
Section 1:
To determine: The angular frequency of the particle.
Answer: The angular frequency of the particle is
Given information:
The position of the particle is
The formula for the acceleration of the particle is,
Substitute
Section 2:
To determine: The amplitude of the motion.
Answer: The amplitude of the motion is
Given information:
The position of the particle is
The general form of position of the particle is,
At the time
Substitute
The general form of velocity of the particle is,
Substitute
Solve the equation (I) and equation (II) to obtain value of
Section 3:
To determine: The phase constant of the motion.
Answer: The phase constant of the motion is
Given information:
The position of the particle is
Substitute
Section 4:
To determine: The position of the particle in simple harmonic motion for
Answer: The position of the particle in simple harmonic motion for
Given information:
The position of the particle is
The formula for the position of the particle is,
Substitute
Conclusion:
Therefore, the position of the particle in simple harmonic motion for
(d)
The velocity of the particle in simple harmonic motion for
(d)

Answer to Problem 11P
The velocity of the particle in simple harmonic motion for
Explanation of Solution
Given information:
The position of the particle is
The general form of velocity of the particle is,
Substitute
Conclusion:
Therefore, the velocity of the particle in simple harmonic motion for
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Chapter 12 Solutions
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