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phyhw16 - valdez(vv689 Homework 16 orin(58140 This...

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valdez (vv689) – Homework 16 – florin – (58140) 1 This print-out should have 11 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points When a body executes simple harmonic mo- tion, its period is 1. the reciprocal of its speed. 2. proportional to its amplitude. 3. inversely proportional to its accelera- tion. 4. proportional to its acceleration. 5. independent of its amplitude. correct Explanation: The period of simple harmonic motion is the same regardless of the amplitude. 002 10.0 points A particle oscillates up and down in simple harmonic motion. Its height y as a function of time t is shown in the diagram. 1 2 3 4 5 5 5 y (cm) t (s) At what time t in the period shown does the particle achieve its maximum positive ac- celeration? 1. None of these; the acceleration is con- stant. 2. t = 3 s 3. t = 1 s correct 4. t = 2 s 5. t = 4 s Explanation: This oscillation is described by y ( t ) = - sin parenleftbigg π t 2 parenrightbigg , v ( t ) = d y dt = - π 2 cos parenleftbigg π t 2 parenrightbigg a ( t ) = d 2 y dt 2 = parenleftBig π 2 parenrightBig 2 sin parenleftbigg π t 2 parenrightbigg . The maximum acceleration will occur when sin parenleftbigg π t 2 parenrightbigg = 1, or at t = 1 s . From a non-calculus perspective, the veloc- ity is negative just before t = 1 s since the particle is slowing down. At t = 1 s, the par- ticle is momentarily at rest and v = 0. Just after t = 1 s , the velocity is positive since the particle is speeding up. Remember that a = Δ v Δ t , acceleration is a positive maximum because the velocity is changing from a nega- tive to a positive value. 003 10.0 points Simple harmonic motion can be described us- ing the equation x = x m sin( ωt + φ ) . If x 0 = initial position, v 0 = initial velocity, then 1. tan φ = + ω x 0 v 0 correct 2. tan φ = - ω x 0 v 0 3. tan φ = + v 0 ω x 0 4. tan φ = - v 0 ω x 0 Explanation: x = x m sin( ω t + φ ) v = d x dt = x m ω cos( ω t + φ ) When t = 0, x 0 = x m sin φ
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valdez (vv689) – Homework 16 – florin – (58140) 2 v 0 = x m ω cos φ x m sin φ x m ω cos φ = x 0 v 0 tan φ = ω x 0 v 0 .
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