Concept explainers
(a)
The position, velocity and acceleration of each of the simple harmonic oscillator’s at time
(a)
Answer to Problem 6PQ
At
Explanation of Solution
Write the expression for the acceleration of the simple harmonic oscillator.
Here,
Write the general equation of acceleration of a simple harmonic oscillator.
Here,
Write the relation between maximum acceleration and amplitude.
Here,
Write the expression for the velocity of simple harmonic oscillator.
Here,
Write the expression for the maximum velocity.
Put equation (V) in (IV) to get relation of
Write the expression for the displacement of the simple harmonic oscillator.
Here,
Conclusion:
Compare equation (I) and (II) to get
Compare equation (I) and (II) to get
Compare equation (I) and (II) to get
Substitute
Substitute
Substitute
Consider
Substitute
Substitute
Substitute
Therefore, at
(b)
The position, velocity and acceleration of simple harmonic oscillator at
(b)
Answer to Problem 6PQ
At
Explanation of Solution
Use equation (I) to calculate acceleration, equation (VIII) to calculate velocity and equation (IX) to calculate position of simple harmonic oscillator at
Conclusion:
Consider
Substitute
Substitute
Substitute
Therefore, at
(c)
The position, velocity and acceleration of simple harmonic oscillator at
(c)
Answer to Problem 6PQ
At
Explanation of Solution
Use equation (I) to calculate acceleration, equation (VIII) to calculate velocity and equation (IX) to calculate position of simple harmonic oscillator.
Conclusion:
Consider
Substitute
Substitute
Substitute
Therefore, at
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Chapter 16 Solutions
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