009A Sample Midterm 1, Problem 5
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The displacement from equilibrium of an object in harmonic motion on the end of a spring is:
where is measured in feet and
is the time in seconds.
Determine the position and velocity of the object when
ExpandFoundations: |
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What is the relationship between position |
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Solution:
ExpandStep 1: |
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To find the position of the object at |
we need to plug |
Thus, we have |
|
ExpandStep 2: |
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Now, to find the velocity function, we need to take the derivative of the position function. |
Thus, we have |
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Therefore, the velocity of the object at time |
|
ExpandFinal Answer: |
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position is |
velocity is |