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hw33 - Muraj Hamza Homework 33 Due 4:00 am Inst Florin This...

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Muraj, Hamza – Homework 33 – Due: Apr 24 2006, 4:00 am – Inst: Florin 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 Given: Simple Harmonic Motion can be de- scribed using the equation y = A sin( k x - ω t - φ ) . Hint: sin( - θ ) = - sin θ . Consider the simple harmonic motion given by the figure. + A -A y 0 π 2 π 3 π 4 π At position x = 0, we have ω t This motion is described by 1. y = A tan - ω t - π 2 · 2. y = A cos - ω t - π 2 · 3. y = A cos - ω t + π 2 · 4. y = A sin - ω t - 3 π 2 5. y = A sin - ω t - π 2 · correct 6. y = A tan - ω t + π 2 · 7. y = A tan - ω t - 3 π 2 8. y = A sin - ω t + π 2 · 9. y = A cos - ω t - 3 π 2 Explanation: If the y -axis is moved such that the angle - ω t - π 2 = 0 , the curve is the sine function A sin( - ω t ) ; therefore y = A sin - ω t - π 2 · is the curve in the figure. 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, x ( t ) = A sin( ω t + φ ) . If A = 4 . 3 m, ω = 2 . 4 rad / s, and φ = 1 . 0472 rad, what is the acceleration of the body at t = 3 s? Note: The argument of the sine function is given here in radians rather than degrees. Correct answer: - 22 . 8777 m / s 2 . Explanation: x = A sin( ω t + φ ) v = dx dt = ω A cos( ω t + φ ) a = dv dt = - ω 2 A sin( ω t + φ ) The basic concepts above are enough to solve the problem. Just use the formula for a ob- tained by differentiating x twice: a = - ω 2 A sin( ω t + φ ) = - 22 . 8777 m / s 2 The phase φ (given in radians) incorporates the initial condition where the body started ( t = 0), meaning it started at x 0 = A sin φ = 3 . 72391 m and it is now at x = A sin( ω t + φ ) = 3 . 97183 m (These two last facts are not needed to solve the problem but clarify the physical picture.) 003 (part 1 of 3) 10 points
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