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HW 014 - hanna(brh687 hk 14 Opyrchal(11105 This print-out...

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hanna (brh687) – hk 14 – Opyrchal – (11105) 1 This print-out should have 5 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 = 5 m, ω = 3 . 477 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: - 41 . 3256 m / s 2 . Explanation: Let : A = 5 m , ω = 3 . 477 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 ) = - (3 . 477 rad / s) 2 (5 m) × sin[(3 . 477 rad / s)(4 s) + 1 . 0472 rad] = - 41 . 3256 m / s 2 . 002 10.0 points Military specifications often call for electronic devices to be able to withstand accelerations of 10 g . To make sure that their products meet this specification, manufacturers test them using a shaking table that can vibrate a device at various specified frequencies and amplitudes.
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