webct9 - SHM maxima 1. The graph below represents the...

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SHM maxima 1. The graph below represents the position of an object as a function of time. At which of the points A-D does the object have its maximum speed? a. A b. B *c. C d. D The maximum speed corresponds to the points which maximum slope in the x-t curve. Since this is a sine function, this happens wherever the function intersects the x axis. Thus the answer is point C. 2. At that point, the velocity is: a. Positive. *b. Negative. The slope at point C is negative. 3. At which of the points A-D does the object have zero speed? *a. A b. B c. C
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d. D The speed is zero at points where the slope in the x - t curve is zero. This happens at all the maxima and minima of the function. This is the case for point A. 4. At which of the points A-D does the object have the maximum acceleration (in magnitude)? *a. A b. B c. C d. D The acceleration corresponds to the curvature of the x-t curve. The curvature is maximum in the graph given above at the minima and maxima. Also, if this is a sine function, the system is undergoing SHM, which means it is subject to a net force F x ∝− , which also means ax ∝ − due to Newton’s second law. Thus the maximum acceleration is found when the distance to the origin is also maximum. 5. At that point, the acceleration is: a. Positive. *b. Negative. When the curve opens down, as in point A, 2 2 0 dx dt < , so the acceleration is negative at the point A. Also, a little before A, the slope (ie, the velocity) is positive, whereas a little after A, the slope (ie, the velocity) is negative. The velocity is thus going from + to 0 to -. This means that the acceleration is negative. 6. At which of the points A-D does the object have zero acceleration? a. A b. B *c. C d. D The acceleration is zero whenever the curvature of the x - t function is zero. This happens whenever the curvature goes from positive to negative or viceversa. This is what happens at point C.
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Also, since ax ∝− , the acceleration is zero when the particle is at x = 0. 7. At which of the points A-D is the object at the maximum distance from the equilibrium position? *a. A b. B c. C d. D The maximum distance from the center is achieved at any of the maxima or minima of the x-t function, like at point A. 8. At that point, the position is: *a. Positive. b. Negative. At point A, x is positive. 9. At which of the points A-D is the object at zero distance from the equilibrium position? a. A b. B *c. C d. D The object is at zero distance from the equilibrium position at point C, which corresponds to x = 0.
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SHM phase 1. The following graph describes the position of an object in a simple harmonic motion given by the equation x ( t ) = A cos( ω t + φ ).
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This homework help was uploaded on 03/26/2008 for the course PHYS 221 taught by Professor Herrera-siklody during the Spring '08 term at Iowa State.

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webct9 - SHM maxima 1. The graph below represents the...

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