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PH101 HW Waves

PH101 HW Waves - This print-out should have 23 questions...

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This print-out should have 23 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 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 = 4 s 5. t = 2 s Explanation: This oscillation is described by y ( t ) = - sin π t 2 , v ( t ) = d y dt = - π 2 cos π t 2 a ( t ) = d 2 y dt 2 = π 2 2 sin π t 2 . The maximum acceleration will occur when sin π t 2 = 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. 002 10.0 points A 128 N object vibrates with a period of 4.76 s when hanging from a spring. What is the spring constant of the spring? The acceleration of gravity is 9 . 81 m / s 2 . Correct answer: 22 . 7346 N / m. Explanation: Let : F g = 128 N , T = 4 . 76 s , and g = 9 . 81 m / s 2 . T = 2 π m k T 2 π 2 = m k k = m 2 π T 2 = F g g 2 π T 2 = 128 N 9 . 81 m / s 2 2 π 4 . 76 s 2 = 22 . 7346 N / m . 003 10.0 points A 52 . 2 g object is attached to a horizontal spring with a spring constant of 14 . 8 N / m and released from rest with an amplitude of 25 . 1 cm. What is the velocity of the object when it is halfway to the equilibrium position if the surface is frictionless? Correct answer: 3 . 66016 m / s.

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Explanation: Let : m = 52 . 2 g = 0 . 0522 kg , k = 14 . 8 N / m , and A = 25 . 1 cm = 0 . 251 m . The speed is v = k m ( A 2 - x 2 ) = 14 . 8 N / m 0 . 0522 kg [(0 . 251 m) 2 - (0 . 1255 m) 2 ] = 3 . 66016 m / s . 004 (part 1 of 3) 10.0 points A 541 g mass is connected to a light spring of force constant 3 N / m that is free to oscillate on a horizontal, frictionless track. The mass is displaced 6 cm from the equilibrium point and released from rest.
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