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  

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


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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