[1pt] A mass is vibrating at the end of a spring with a spring constant 2.66 N/m

Question

[1pt] A mass is vibrating at the end of a spring with a spring constant 2.66 N/m. The figure shows a graph of its position x (in centimetres) as a function of time t (in seconds). At what time between t=0 s and the first maximum after t=0 s is the mass not moving? http://www.learning.physics.dal.ca/dalphysicslib/Graphics/Gtype27/prob01.8.gif [1pt] What is the magnitude of the acceleration of the object at the second maximum in the x-t curve after t = 0 s? Answer: 14. [1pt] What is the mass of the object? Answer: 15. [1pt] How much energy did the system originally contain? Correct: 4.79e-03 J 16. [1pt] How much energy did the system lose between t = 0 s and the third maximum after t = 0 s? Think about where this energy has gone. Answer:

Explanation / Answer

So I guess I'll answer the questions that do not have answers already.

The mass is not moving at the first minimum, at .8 seconds.

The oscillation appears to have period = 1.6 s, so = 2/1.6 = 3.93 s-1, so the acceleration (the second derivative of position) at 3.2, .027 is .027*2 = .416 m/s/s.

The mass of the object is m = f/a = kx/a = 2.66*.027/.416 = 172 grams.

The system originally contained kx2/2 = 4.79 x 10^-3 J.

The system lost 1/2kx2 - 1/2kxI2 = 2.66*(.062- .0182)/2 = 4.36 x 10^-3 J. This energy has been dissipated, most likely as heat, by the damping force.

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