HW9 Solution

HW9 Solution - lew (dl9564) hk9 Opyrchal (41104) 1 This...

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Unformatted text preview: lew (dl9564) hk9 Opyrchal (41104) 1 This print-out should have 9 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points A body oscillates with simple harmonic mo- tion along the x-axis. Its displacement varies with time according to the equation A = A sin parenleftBig t + 3 parenrightBig , where = radians per second, t is in sec- onds, and A = 6 m. What is the phase of the motion at t = 8 . 8 s? Correct answer: 28 . 6932 rad. Explanation: Let : t = 8 . 8 s and = . x = A sin( t + ) The phase is the angle in the argument of the sine function, and from the problem state- ment we see it is = t + 3 = ( rad / s) (8 . 8 s) + 3 = 28 . 6932 rad . 002 (part 1 of 4) 10.0 points A 15 . 3 kg mass is suspended on a 1 10 5 N / m spring. The mass oscillates up and down from the equilibrium position y eq = 0 according to y ( t ) = A sin( t + ) . Find the angular frequency of the oscillat- ing mass. Correct answer: 80 . 8452 s 1 . Explanation: Let : M = 15 . 3 kg and k = 1 10 5 N / m . When the mass moves out of equilibrium, it suffers a net restoring force F net y = F spring Mg = k ( y y eq ) = ky , and accelerates back towards the equilibrium position at the rate a y = F net y M = k M y . Therefore, the mass oscillates harmonically with angular frequency = radicalbigg a y y = radicalbigg k M = radicalBigg 1 10 5 N / m 15 . 3 kg = 80 . 8452 s 1 ....
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This note was uploaded on 01/22/2009 for the course PHYS Phys 106 taught by Professor Opyrachal during the Fall '08 term at NJIT.

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HW9 Solution - lew (dl9564) hk9 Opyrchal (41104) 1 This...

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