Slide 1 Fig. 15.1, p.453

Active Figure 15.1

Slide 2 Fig. 15.2, p.455

Slide 3 Fig. 15.2a, p.455

Slide 4 Fig. 15.2b, p.455

Slide 5 Fig. 15.3, p.456

Slide 6 Fig. 15.4, p.456

Slide 7 Fig. 15.5, p.456

Slide 8 Fig. 15.5a, p.456

Slide 9 Fig. 15.5b, p.456

Slide 10 Fig. 15.6, p.458

Slide 11 Fig. 15.7, p.458

Active Figure 15.1 ActiveFigure 15.7 T does not depend on A

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

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

Slide 14 Fig. 15.8, p.459

Active Figure 15.2ActiveFigure 15.7 Active 15.9

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

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

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

(d) T/2

Slide 18

Answer: (b). According to Equation 15.13, the period is proportional to the square root of the mass.

Quick Quiz 15.5

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

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

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

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,

2

1 62 2 2 ~ s ~ 2s

9.8 m/s 3

m x mT

k g

QUICK QUIZ 15.1 ANSWER

Slide 23 Fig. 15.9, p.459

Slide 24 Fig. 15.10, p.462

Active 15.10

Slide 25 Fig. 15.10a, p.462

Slide 26 Fig. 15.10b, p.462

Slide 27 Fig. 15.11, p.463

Slide 28 Fig. 15.12, p.464

Slide 29 Fig. 15.14, p.465

Af 15.14

Slide 30 Fig. 15.15, p.466

Slide 31 Fig. 15.15a, p.466

Slide 32 Fig. 15.15b, p.466

Slide 33 Fig. 15.15c, p.466

Slide 34 Fig. 15.15d, p.466

Slide 35 Fig. 15.16, p.467

Slide 36 Fig. 15.17, p.468

AF 15.11

AF 15.17

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

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

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

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

Slide 41 Fig. 15.18, p.469

Slide 42 Fig. 15.19, p.470

Slide 43 Fig. 15.20, p.470

Slide 44 Fig. 15.21, p.471

AF 15.22

Slide 45 Fig. 15.22, p.471

Slide 46 Fig. 15.23, p.471

Slide 47 Fig. 15.24a, p.472

Slide 48 Fig. 15.24b, p.472

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

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

Slide 51 Fig. 15.25, p.473

Slide 52 Fig. P15.25, p.478

Slide 53 Fig. P15.26, p.478

Slide 54 Fig. P15.39, p.479

Slide 55 Fig. P15.51, p.480

Slide 56 Fig. P15.52, p.481

Slide 57 Fig. P15.53, p.481

Slide 58 Fig. P15.56, p.481

Slide 59 Fig. P15.59, p.481

Slide 60 Fig. P15.61, p.482

Slide 61 Fig. P15.66, p.482

Slide 62 Fig. P15.67, p.482

Slide 63 Fig. P15.68, p.483

Slide 64 Fig. P15.69, p.483

Slide 65 Fig. P15.71, p.483

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

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

Slide 68 Fig. P15.74, p.484

Slide 69 Fig. P15.75, p.484