A student attaches a block to a vertical spring of unknown spring constant so that the block-spring system will oscillate if the
block-spring system is released from rest at a vertical position that is not the system’s equilibrium position. The student varies the object’s mass and uses a stopwatch to determine the time it takes the object to make one oscillation. The student creates the graph that is shown. The slope of the line of best fit is equal to which of the following quantities?
2 answers:
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Answer:
Explanation:
We should first find the velocity and acceleration functions. The velocity function is the derivative of the position function with respect to time, and the acceleration function is the derivative of the velocity function with respect to time.
Similarly,
Now, the angle between velocity and acceleration vectors can be found.
The angle between any two vectors can be found by scalar product of them:
So,
At time t = 0, this equation becomes