hw19 - khounvivongsy(sk27799 Homework 19 Weathers(17104...

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khounvivongsy (sk27799) – Homework 19 – Weathers – (17104) 1 This print-out should have 12 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 x ( t ) = A sin( ω t + φ ) . If A = 7 m, ω = 2 . 368 rad / s, and φ = 1 . 0472 rad, what is the acceleration of the body at t = 4 s? Note: The argument of the sine function is in radians rather than degrees. Correct answer: 34 . 8817 m / s 2 . Explanation: Let : A = 7 m , ω = 2 . 368 rad / s , φ = 1 . 0472 rad , and t = 4 s . x = A sin( ω t + φ ) v = d x dt = ω A cos( ω t + φ ) a = d v dt = ω 2 A sin( ω t + φ ) = ω 2 A sin( ω t + φ ) = (2 . 368 rad / s) 2 (7 m) × sin[(2 . 368 rad / s)(4 s) + 1 . 0472 rad] = 34 . 8817 m / s 2 . 002 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 0 sin parenleftBig ω t + π 3 parenrightBig , where ω = π radians per second, t is in sec- onds, and A 0 = 3 . 2 m. What is the phase of the motion at t = 2 . 8 s? Correct answer: 9 . 84366 rad. Explanation: Let : t = 2 . 8 s and ω = π . x = A 0 sin( ω t + φ ) The phase is the angle in the argument of the sine function, and from the problem state- ment we see it is φ = π t + π 3 = ( π rad / s) (2 . 8 s) + π 3 = 9 . 84366 rad . 003 10.0 points A horizontal platform vibrates with simple harmonic motion in the horizontal direction with a period of 1 . 45 s. A body on the plat- form starts to slide when the amplitude of vibration reaches 0 . 39 m. Find the coefficient of static friction be- tween body and platform. The acceleration of gravity is 9 . 8 m / s 2 . Correct answer: 0 . 747244. Explanation: Let : T = 1 . 45 s , A max = 0 . 39 m , and g = 9 . 8 m / s 2 . At each instant, there are two forces acting on the platform: the force responsible for the oscillation F = kx and the force of friction F s = μ N between the body and the platform. Applying Newton’s second law horizontally, summationdisplay F x = kx + F s = m a platform
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khounvivongsy (sk27799) – Homework 19 – Weathers – (17104) 2 The only force acting on the block in the horizontal direction is the frictional force, so F s = m a block If the block does not slide, its acceleration is the same as the platform: a block = a platform set = a The force of friction is F s = μ N = μ m g and from simple harmonic motion x = A cos ωt .
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