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(a)
The motion of the object, where the displacement
(a)
![Check Mark](/static/check-mark.png)
Answer to Problem 15AYU
Solution:
The motion of the object modeled by the displacement function
Explanation of Solution
Given information:
The displacement
Explanation:
In simple harmonic motion, an object that moves on a coordinate axis, so that the displacement
By comparing
Therefore, motion of the object is simple harmonic.
(b)
To calculate: The maximum displacement of the object from its rest position, where the displacement
(b)
![Check Mark](/static/check-mark.png)
Answer to Problem 15AYU
Solution:
The maximum displacement of the object from its rest position is
Explanation of Solution
Given information:
The displacement
Formula used:
In simple harmonic motion, the displacement
Calculation:
The maximum displacement of the object from its rest position is the amplitude.
Compare
The maximum displacement of the object from its rest position is
Therefore, the maximum displacement of the object from its rest position is
(c)
To calculate: The time required for one oscillation, where the displacement
(c)
![Check Mark](/static/check-mark.png)
Answer to Problem 15AYU
Solution:
The time required for one oscillation is
Explanation of Solution
Given information:
The displacement
Formula used:
In simple harmonic motion, the displacement
Calculation:
The time required for one oscillation is period.
Compare
Substitute
Thus, period is
Therefore, the time required for one oscillation is
(d)
To calculate: Frequency of an object, where the displacement
(d)
![Check Mark](/static/check-mark.png)
Answer to Problem 15AYU
Solution:
The frequency of an object is
Explanation of Solution
Given information:
The displacement
Formula used:
In simple harmonic motion, the displacement
Calculation:
From part (c),
The frequency is defined as
Thus, there is one oscillation per second.
Therefore, the frequency of an object is
Chapter 8 Solutions
Precalculus
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