Question 1119169: A mass is attached to a spring at one end and secured to a wall at the other end. When the mass is pulled away from the wall and released, it moves back and forth (oscillates) along the floor.
If there is no friction between the mass and the floor, and no drag from the air, then the displacement of the mass versus time could be modelled by a sinusoidal function. Because of friction, however, the speed of the mass is reduced, which causes the displacement to decrease exponentially with each oscillation.
The displacement function d(t) is a combination of functions: d(t) 5 f (t)g(t) 1 r.
Consider the following situation:
• The mass is at a resting position of r 5 30 cm.
• The spring provides a period of 2 s for the oscillations.
• The mass is pulled to d 5 50 cm and released. • After10s,thespringisatd533cm.
A. Make a sketch of the displacement versus time graph to ensure that you understand this situation.
B. Write the general equation of the function that models this situation, with the necessary parameters.
C. Use the information provided to determine the values of the parameters, and write the equation of the model.
D. Graph the function you determined in part C using graphing technology. Check that it models the motion of the mass correctly.
E. Write the function for displacement that would be correct if there were no damping of the motion due to friction.
F. Calculate the displacement at 7.7 s for each model you determined in parts C and E, and compare your results.
G. Estimate the instantaneous speed of the mass at 7.7 s for each model, and compare your results.
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13195)   (Show Source):
You can put this solution on YOUR website!
Since nobody has responded in the several days since you posted this question, I will comment....
(1) There are a few people here who can solve physics problems like this; but this site is primarily for math problems.
(2) Much of your nomenclature is, at least to my knowledge, not standard; so we would have to try to guess what the given information is, and what the various parts of the problem are asking.
(3) But before we even get to trying to understand the problem, if we read the problem as you have shown it, then there is no oscillation. That is because you initially say the mass is secured to the wall, and then you say the mass is pulled away from the wall.
So there is now a hole in the wall where the mass was secured, and the mass is on the floor, not moving, with the spring attached to it.... Experiment over.
If you want help with the problem, try re-posting with the problem correctly described, and with the parts of the question clearly stated.
Answer by ikleyn(52748)  (Show Source):
You can put this solution on YOUR website! .
1. I can solve (practically) any school Physics problem, as soon as it is formulated reasonably, accurately, professionally and correctly.
2. I have a great practice of solving such problems. (having solved hundreds, if not thousands, of them)
3. I never saw a professionally formulated physics problem longer than 5 lines of the standard text.
4. I am absolutely sure that any formulation of a Physics problem longer than 5 lines is a) unreasonable; b) unprofessional and c) incorrect.
5. In the given concrete case, the problem says that the period is 2 seconds and friction is absent, so we have harmonic oscillations.
6. From the other side, the condition says that after 10 seconds (5 periods (!)) the spring sat 533 cm, while it must be 550 cm.
7. So, the condition is self-contradictory.
8. It shows, demonstrates, displays, highlights and confirms that the condition is a) nonsensical; b) unprofessional and c) incorrect.
9. It is not my duty in this forum to explain every author where he (or she) is wrong.
// In opposite, it is the visitor's duty to provide the correct input.
10. It is why I didn't touch this problem.
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In my text, do not consider this "figure of speech" "5 lines" as a world universal constant.
It might be 6 or 7 lines, but not more than 10 lines.
11 lines is just far above any reasonable limit.
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