1. Tuesday(11/09): Introduction to Chap. 10, The Ideal Spring and

Simple Harmonic Motion. Energy and Simple Harmonic Motion, the Simple

Pendulum, Damped vs. Driven Oscillators. HW: Read pages 267-280 and

solve prob. 3, 4, 5, 8, 10, and 18 on pages 292-3.

2. Wednesday(11/10): Elastic Deformation, Stress, Strain, and Hooke's

Law. HW: Read pages 280-291 and solve prob. 24, 34, 42, 50, and 63 on

pages 294-6.

3. Thursday(11/11):  LAB on the Simple Pendulum. HW: Process Lab data.

Lab report is due on Monday.

4. Friday(11/12): Post-Lab Discussion and Review I for Chapter 10 -

Simple Harmonic Motion and Elasticity. HW: Complete Lab report and

Review Problems on lab handout.

5. Monday(11/15): Review II for Chapter 10 - Simple Harmonic Motion

and Elasticity. HW: Complete handout.

6. Tuesday(11/16): TEST on Ch.10. HW: Go to web-site for notes

on Ch.11 - Fluids.

1. A very special kind of motion occurs when the force on a body is

proportional to the displacement of the body from equilibrium. If this

force always acts toward the equilibrium position of the body, there

is a repetitive back-and-forth motion about this position.

2. Such motion is an example of what is called periodic or oscillatory

motion. You are most likely familiar with several examples of periodic

motion, such as the oscillations of a mass on a spring, the motion of a

pendulum, and the vibrations of a stringed musical instrument.

3. Most of the material in this chapter deals with idealized periodic

motion, called Simple Harmonic Motion (SHM). In this type of motion,

an object oscillates between two spatial positions for an indefinite

period of time with no loss in mechanical energy.

4. In real mechanical systems, retarding (frictional) forces are always

present and these forces are considered in section 10.5 of the chapter.

We call these systems "Damped Harmonic Oscillators." Consequently, in

order to maintain their motion they must be "driven", hence the term

"Driven Harmonic Motion" in section 10.6.

5. The most common system which undergoes simple harmonic motion

is the mass-spring system. The mass is assumed to move on a horizontal,

frictionless surface while the spring is fastened to a wall. Or, the spring

can be hung from a beam and the mass is attached to the free end of

the spring.

6. The point x = 0 is the equilibrium position of the mass; that is, the

point where the mass would reside if left undisturbed. In this position,

there is no net force on the mass.

7. When the mass is displaced a distance x from its equilibrium position,

the spring produces a linear restoring force given by Hooke's Law,

F = -kx, where k is the force constant of the spring, and has units of N/m.

8. This law is named after Robert Hooke, a British scientist and

mathematician who lived from 1635 to 1703, and was a contemporary of

Isaac Newton. In simple terms, Hooke's Law states that the force required

to stretch a spring is directly proportional to the distance stretched, as

long as the elastic limit is not exceeded.

9. The minus sign in F = -kx means that F is to the left when the

displacement x is positive, whereas F is to the right when x is negative.

In other words, the direction of the force F is always towards the

equilibrium position.

10. If a graph of F versus x is plotted, the slope will be k, the elastic

constant. It also should be apparent that the area under the graph

represents the work done in stretching the spring. In fact,

12. In particular, notice that when the displacement is a maximum, the

energy of the system is entirely potential energy; whereas, when the

displacement is zero, the energy is entirely kinetic energy.

13. This is consistent with the fact that v = 0 when x = A, the amplitude,

or maximum displacement from the equilibrium position. And it follows

that v = v_max , when x = 0. For an arbitrary value of x, the energy is the

sum of K and U.

14. When the angular displacement is small during the entire motion (less

than about 10 degrees), the pendulum exhibits SHM. In this case, the

resultant force acting on the mass m equals the component of weight

tangent to the arc, and has a magnitude F = mg·sin(θ).

15. Since this force is always directed towards θ = 0, it corresponds to a

restoring force. For small θ, we use the approximation that sin(θ) = θ.

16. In other words, the period depends only on the length of the pendulum

and the acceleration of gravity. The period does not depend on mass, so we

conclude that all simple pendula of equal length oscillate with the same

17. Period and frequency are reciprocal quantities. T = 1/f . And using the

18. Similarly, it can be shown that the maximum speed of an object in SHM is

given by v_max = Aω . Also the maximum acceleration is, a_max = Aω² . Another

way to express angular frequency is ω = √(k/m) .

19. The last sections of this chapter deals with the realistic situation of objects

that deform under load conditions. Such deformations are usually elastic in

nature and do not affect the conditions of equilibrium.

20. By elastic we mean that when the deforming forces are removed, the object

returns to its original shape. Several elastic constants are defined, each

corresponding to a different type of deformation.

21. The elastic properties of solids are described in terms of stress and strain.

Stress is a quantity that is proportional to the force causing a deformation of the

object. Strain is a measure of the degree of the resulting deformation.

22. The elastic modulus of a material is the ratio of stress to strain for that

material. There is an elastic modulus for each of the three types of deformation:

(i) Young's modulus which measures resistance to change in length,

Y = (F/A)/(ΔL/L_o) , (ii) Shear modulus which measures resistance to relative

motion of the planes of a solid, and (iii) Bulk modulus which measures the

resistance to a change in volume.

23. And still, we need these steps to solve any problem in Physics:

(i) read the problem and identify the given variables

(ii) determine what you are asked to solve for

(iii) find the correct equation to use

(iv) use Algebra, Trigonometry, and/or Calculus to isolate the unknown

(v) substitute-in the given information and simplify.

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THE AP PHYSICS B ARCHIVES Ch.1: Physics Intro. Ch.2: Linear Motion. Ch.3: 2-Dim Motion. Ch.4&5: Newton's Laws. Ch.6: Work/Energy. Ch.7: Momentum. Ch.8&9: Rotary Motion. Ch.10: SHM. Ch.11: Fluids. Ch.12&13: Temp.&Heat. Ch.14&15: Thermodynamics. Semester Review.