Difference between revisions of "009A Sample Midterm 1, Problem 5"

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(Created page with "<span class="exam">The displacement from equilibrium of an object in harmonic motion on the end of a spring is: ::<span class="exam"><math>y=\frac{1}{3}\cos(12t)-\frac{1}{4}\...")
 
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|What is the relationship between position &nbsp;<math style="vertical-align: -5px">s(t)</math>&nbsp; and velocity &nbsp;<math style="vertical-align: -5px">v(t)</math>&nbsp; of an object?
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|What is the relationship between the position &nbsp;<math style="vertical-align: -5px">s(t)</math>&nbsp; and the velocity &nbsp;<math style="vertical-align: -5px">v(t)</math>&nbsp; of an object?
 
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|&nbsp; &nbsp; &nbsp; &nbsp; <math>v(t)=s'(t)</math>
 
|&nbsp; &nbsp; &nbsp; &nbsp; <math>v(t)=s'(t)</math>

Revision as of 19:24, 13 April 2017

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  


Foundations:  
What is the relationship between the position    and the velocity    of an object?
       


Solution:

Step 1:  
To find the position of the object at  
we need to plug    into the equation  
Thus, we have
       
Step 2:  
Now, to find the velocity function, we need to take the derivative of the position function.
Thus, we have
       
Therefore, the velocity of the object at time    is
       


Final Answer:  
        position is  
        velocity is  

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