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Unformatted text preview: Gozick, Brandon Homework 11 Due: Oct 17 2006, 7:00 pm Inst: D Weathers 1 This print-out should have 11 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 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( t + ) . If A = 3 . 3 m, = 2 . 1 rad / s, and = 1 . 0472 rad, what is the acceleration of the body at t = 1 s? Note: The argument of the sine function is given here in radians rather than degrees. Correct answer: 0 . 0815676 m / s 2 . Explanation: x = A sin( t + ) v = dx dt = A cos( t + ) a = dv dt =- 2 A sin( t + ) The basic concepts above are enough to solve the problem. Just use the formula for a ob- tained by differentiating x twice: a =- 2 A sin( t + ) = 0 . 0815676 m / s 2 The phase (given in radians) incorporates the initial condition where the body started ( t = 0), meaning it started at x = A sin = 2 . 85788 m and it is now at x = A sin( t + ) =- . 0184961 m (These two last facts are not needed to solve the problem but clarify the physical picture.) keywords: 002 (part 1 of 1) 10 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( t + / 3) , where = radians per second, t is in sec- onds, and A = 2 m. What is the phase of the motion at t = 9 s? Correct answer: 29 . 3215 rad. Explanation: Basic Concepts: 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 = h ( rad / s)(9 s) + 3 i = 29 . 3215 rad . keywords: 003 (part 1 of 3) 10 points A block of unknown mass is attached to a spring of spring constant 3 . 12 N / m and undergoes simple harmonic motion with an amplitude of 4 . 47 cm. When the mass is halfway between its equilibrium position and the endpoint, its speed is measured to be v = 20 . 1 cm / s....
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