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Slide 1Fig. 15.1, p.453 Active Figure 15.1

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Slide 2Fig. 15.2, p.455

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Slide 3Fig. 15.2a, p.455

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Slide 4Fig. 15.2b, p.455

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Slide 5Fig. 15.3, p.456

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Slide 6Fig. 15.4, p.456

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Slide 7Fig. 15.5, p.456

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Slide 8Fig. 15.5a, p.456

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Slide 9Fig. 15.5b, p.456

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Slide 10Fig. 15.6, p.458

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Slide 11Fig. 15.7, p.458 Active Figure 15.1 ActiveFigure 15.7 T does not depend on A

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Slide 12 Quick Quiz 15.1 A block on the end of a spring is pulled to position x = A and released. In one full cycle of its motion, through what total distance does it travel? (a) A/2 (b) A (c) 2A (d) 4A

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Slide 13 Answer: (d). From its maximum positive position to the equilibrium position, the block travels a distance A. It then goes an equal distance past the equilibrium position to its maximum negative position. It then repeats these two motions in the reverse direction to return to its original position and complete one cycle. Quick Quiz 15.1

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Slide 14Fig. 15.8, p.459 Active Figure 15.2 ActiveFigure 15.7ActiveFigure 15.7 Active 15.9Active 15.9

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Slide 15 Quick Quiz 15.4 Consider the graphical representation below of simple harmonic motion, as described mathematically in Equation 15.6. When the object is at position A on the graph, its (a) velocity and acceleration are both positive (b) velocity and acceleration are both negative (c) velocity is positive and its acceleration is zero (d) velocity is negative and its acceleration is zero (e) velocity is positive and its acceleration is negative (f) velocity is negative and its acceleration is positive

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Slide 16 Answer: (a). The velocity is positive, as in Quick Quiz 15.2. Because the spring is pulling the object toward equilibrium from the negative x region, the acceleration is also positive. Quick Quiz 15.4

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Slide 17 Quick Quiz 15.5 An object of mass m is hung from a spring and set into oscillation. The period of the oscillation is measured and recorded as T. The object of mass m is removed and replaced with an object of mass 2m. When this object is set into oscillation, the period of the motion is (a) 2T (b) 2T (c) T (d) T/2

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Slide 18 Answer: (b). According to Equation 15.13, the period is proportional to the square root of the mass. Quick Quiz 15.5

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Slide 19 Quick Quiz 15.6 The figure shows the position of an object in uniform circular motion at t = 0. A light shines from above and projects a shadow of the object on a screen below the circular motion. The correct values for the amplitude and phase constant of the simple harmonic motion of the shadow are (a) 0.50 m and 0 (b) 1.00 m and 0 (c) 0.50 m and π (d) 1.00 m and π

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Slide 20 Answer: (c). The amplitude of the simple harmonic motion is the same as the radius of the circular motion. The initial position of the object in its circular motion is π radians from the positive x axis. Quick Quiz 15.6

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Slide 21 You hang an object onto a vertically hanging spring and measure the stretch length of the spring to be 1 meter. You then pull down on the object and release it so that it oscillates in simple harmonic motion. The period of this oscillation will be a) about half a second, b) about 1 second, c) about 2 seconds, or d) impossible to determine without knowing the mass or spring constant. (end of section 15.2) QUICK QUIZ 15.1

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Slide 22 (c). This problem illustrates an easy method for determining the properties of a spring-object system. When you hang the object, the spring force, kx, will be equal to the weight, mg, so that kx = mg or x/g = m/k. From Equation 15.13, QUICK QUIZ 15.1 ANSWER

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Slide 23Fig. 15.9, p.459

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Slide 24Fig. 15.10, p.462 Active 15.10

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Slide 25Fig. 15.10a, p.462

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Slide 26Fig. 15.10b, p.462

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Slide 27Fig. 15.11, p.463

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Slide 28Fig. 15.12, p.464

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Slide 29Fig. 15.14, p.465 Af 15.14

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Slide 30Fig. 15.15, p.466

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Slide 31Fig. 15.15a, p.466

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Slide 32Fig. 15.15b, p.466

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Slide 33Fig. 15.15c, p.466

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Slide 34Fig. 15.15d, p.466

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Slide 35Fig. 15.16, p.467

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Slide 36Fig. 15.17, p.468 AF 15.11 AF 15.17

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Slide 37 Quick Quiz 15.7 A grandfather clock depends on the period of a pendulum to keep correct time. Suppose a grandfather clock is calibrated correctly and then a mischievous child slides the bob of the pendulum downward on the oscillating rod. Does the grandfather clock run (a) slow (b) fast (c) correctly

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Slide 38 Answer: (a). With a longer length, the period of the pendulum will increase. Thus, it will take longer to execute each swing, so that each second according to the clock will take longer than an actual second – the clock will run slow. Quick Quiz 15.7

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Slide 39 Quick Quiz 15.8 Suppose a grandfather clock is calibrated correctly at sea level and is then taken to the top of a very tall mountain. Does the grandfather clock run (a) slow (b) fast (c) correctly

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Slide 40 Answer: (a). At the top of the mountain, the value of g is less than that at sea level. As a result, the period of the pendulum will increase and the clock will run slow. Quick Quiz 15.8

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Slide 41Fig. 15.18, p.469

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Slide 42Fig. 15.19, p.470

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Slide 43Fig. 15.20, p.470

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Slide 44Fig. 15.21, p.471 AF 15.22

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Slide 45Fig. 15.22, p.471

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Slide 46Fig. 15.23, p.471

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Slide 47Fig. 15.24a, p.472

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Slide 48Fig. 15.24b, p.472

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Slide 49 Quick Quiz 15.9 An automotive suspension system consists of a combination of springs and shock absorbers, as shown in the figure below. If you were an automotive engineer, would you design a suspension system that was (a) underdamped (b) critically damped (c) overdamped

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Slide 50 Answer: (a). If your goal is simply to stop the bounce from an absorbed shock as rapidly as possible, you should critically damp the suspension. Unfortunately, the stiffness of this design makes for an uncomfortable ride. If you underdamp the suspension, the ride is more comfortable but the car bounces. If you overdamp the suspension, the wheel is displaced from its equilibrium position longer than it should be. (For example, after hitting a bump, the spring stays compressed for a short time and the wheel does not quickly drop back down into contact with the road after the wheel is past the bump – a dangerous situation.) Because of all these considerations, automotive engineers usually design suspensions to be slightly underdamped. This allows the suspension to absorb a shock rapidly (minimizing the roughness of the ride) and then return to equilibrium after only one or two noticeable oscillations. Quick Quiz 15.9

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Slide 51Fig. 15.25, p.473

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Slide 52Fig. P15.25, p.478

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Slide 53Fig. P15.26, p.478

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Slide 54Fig. P15.39, p.479

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Slide 55Fig. P15.51, p.480

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Slide 56Fig. P15.52, p.481

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Slide 57Fig. P15.53, p.481

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Slide 58Fig. P15.56, p.481

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Slide 59Fig. P15.59, p.481

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Slide 60Fig. P15.61, p.482

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Slide 61Fig. P15.66, p.482

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Slide 62Fig. P15.67, p.482

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Slide 63Fig. P15.68, p.483

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Slide 64Fig. P15.69, p.483

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Slide 65Fig. P15.71, p.483

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Slide 66Fig. P15.71a, p.483

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Slide 67Fig. P15.71b, p.483

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Slide 68Fig. P15.74, p.484

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Slide 69Fig. P15.75, p.484

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