Simple Harmonic Motion UNIT PACKET

Student:

Mr. Khalilian

AP Physics

Due Date:

Simple Harmonic Motion UNIT PACKET

Includes Guides for Notes, HW, and CW

UNIT 6 AGENDA

______Day 1: Introduction to Simple Harmonic Motion

· Do Now, p. 19

· Simple Harmonic Motion Introduction Lab, p. 3

· Note-taking Expectations

· HW: Read Sections 14.1 – 14.4. Take notes in the format of the Notes Outline on p. 4

______Day 2: Spring SHM

· Do Now, p. 18

· Notes Review

· Simple Harmonic Motion I and II, p. 6-7

· HW: Read sections 14.5 – 14.6. Take notes in the format of the Notes Outline on p. 4; Finish CW if necessary

______Day 3: Pendulum SHM

· Do Now, p. 17

· Simple Harmonic Motion III, p. 8

· HW: Pendulums – Maximum Speed of the Bob, p. 9

______Day 4: Final Exam Review

· Final Exam, p. 15

· Introduction to the SHM Lab

· HW: SHM Practice and Review, p. 11: #1-4; Answer each question on a sheet of notebook paper, with an explanation.

______Day 5: SHM Lab, Day 1

· SHM HW Check

· End of Unit Lab, Day 1, p. 10

· HW: SHM Practice and Review, p. 11-12: #5 – 8; Answer each question on a sheet of notebook paper, with an explanation.

______Day 6: SHM Lab, Day 2

· SHM HW Check

· End of Unit Lab, Day 2, p. 10

· HW: SHM Practice and Review, p. 13: #9; Show your thought process clearly.

______Day 7: SHM Review

· Do Now, p. 16

· SHM HW Check

· SHM Practice and Review, p. 14: #10.

· HW: Study for your exam.

______Day 8: SHM Exam

Recommended Book Problems for the Unit: p. 464: 23; p. 465: #1, 5, 7a, 19; p. 466: 25, 29

SIMPLE HARMONIC MOTION INTRODUCTION LAB

In order to investigate simple harmonic motion of a mass on a spring, graphs of force, position, and velocity as a function of time were made. A spring was hung from a force probe at the top of a support rod, as is show in Figure 1. A 100 g mass was attached to the bottom of the spring. Students created simple harmonic motion by pulling the mass approximately 5 cm down and releasing it. As the mass oscillated up and down, students used LoggerPro to create a graph of Force as a function of time. This procedure was repeated until the students had a clean graph. The vertical axis was adjusted, where needed, by clicking a number on the axis, typing the new one, and hitting return. That graph was used to answer the questions in Part I.

Figure 1

To analyze motion graphs of the mass on the spring, students opened a new file in LoggerPro. In the folder “_Physics with Vernier,” they opened the file entitled “15 Simple Harmonic Motion.” Students then repeated the procedure above until they had clean graphs. These graphs were used to answer the questions in Part II.

Part I.

1. Where is the mass in its motion when the force is at a maximum? ______(e.g. top, bottom, middle? On the way up? On the way down?)

2. Where is the mass in its motion when the force is at a minimum? ______

3. Clearly sketch the graph below, labeling your axes. Use your answers to #1-2 to label the locations of the mass at those points.

Part II

4. Where is the mass in its motion when the position is at a maximum? ______(e.g. top, bottom, middle? On the way up? On the way down?)

5. Where is the mass in its motion when the position graph is at a minimum? ______

6. Where is the mass in its motion when the velocity is at a maximum? ______

7. Where is the mass in its motion when the velocity is crossing the horizontal axis? ______

8. Clearly sketch both the position and velocity graphs below. Use your answers to #4-7 to label the locations of the mass at those points.

NOTES OUTLINE

Notes for this unit should be taken in your notebook. You may use either Cornell or Outline style. Both are presented below. (P = paragraph of that section)

Cornell Style / Outline Style
14.1 Equilibrium and Oscillation
Frequency and Period
Oscillatory Motion
14.2 Linear Restoring Forces and SHM
Motion of a Mass on a Spring
Vertical Mass on a Spring
The Pendulum
SKIP 14.3
14.4 Energy in Simple Harmonic Motion
Finding the Frequency for Simple Harmonic Motion
SKIP p. 451 – 452
14.5 Pendulum Motion
SKIP Physical Pendulums and Locomotion
14.6 Damped Oscillations
SKIP p. 456 – 462 / · P1 Connection:
· P1 Concept:
· P2 Connection:
· P2 Concept:
· Rewrite “In general,…” from P2 in own words.
· Connection:
· Concept:
· Translate paragraph à Picture à Graph
· P1 Connection:
· P1 Concept:
· Examples of SHM Concept:
· Connection:
· Concept:
· Connection:
· Concept:
· Answer: How is this section different from the last section?
· End of p. 441 Concept:
· End of section Connection:
· End of section Concept:
· Connection:
· Concept:
· Translate P2 à Figure 14.14
· Connection:
· Concept:
· Connection:
· Concept:
· End of p. 453 Connection:
· End of p. 453 Concept:
· P1-3 Connection:
· P1-3 Concept: / I. 14.1 Equilibrium and Oscillation
a. Intro section
i. P1 Connection:
ii. P1 Concept:
iii. P2 Connection:
iv. P2 Concept:
b. Frequency and Period
i. Rewrite “In general,…” from P2 in own words.
ii. Connection:
iii. Concept:
c. Oscillatory Motion
i. Translate paragraph à Picture à Graph
ii. P1 Connection:
iii. P1 Concept:
iv. Examples of SHM Concept:
II. 14.2 Linear Restoring Forces and SHM
a. Intro section
i. Connection:
ii. Concept:
b. Motion of a Mass on a Spring
i. Connection:
ii. Concept:
c. Vertical Mass on a Spring
i. Answer: How is this section different from the last section?
ii. End of p. 441 Concept:
iii. End of section Connection:
iv. End of section Concept:
d. The Pendulum
i. Connection:
ii. Concept:
III. 14.4 Energy in Simple Harmonic Motion
a. Intro section
i. Translate P2 à Figure 14.14
ii. Connection:
iii. Concept:
b. Finding the Frequency for Simple Harmonic Motion
i. Connection:
ii. Concept:
IV. 14.5 Pendulum Motion
i. End of p.453 Connection:
ii. End of p. 453 Concept:
V. 14.6 Damped Oscillations
i. P1-3 Connection:
ii. P1-3 Concept:

SIMPLE HARMONIC MOTION I – HORIZONTAL SPRING

A spring (k = 200 N/m) is mounted horizontally on a frictionless surface. One end of the spring is attached to a fixed wall, and the other end is attached to a block of mass 2 kg. The block is pulled aside to a distance of 0.04 m and released from rest.

1. Calculate the period and frequency of oscillation of the mass.

2. Compute the maximum velocity of the vibrating mass.

3. Calculate the maximum acceleration.

4. Compute the velocity and acceleration when the body has moved halfway into the center from its initial position.

5. Graph the a) total, b) kinetic, and c) elastic potential energy of the system as a function of position. Graph all of these on the same axis. What is the relationship between the kinetic and potential energies?

SIMPLE HARMONIC MOTION II – VERTICAL SPRING

A body of mass 5kg is suspended by a spring which stretches 0.1 m when the body is attached. The body is then displaced downward an additional 0.05 m and released from rest.

1. Calculate the period, frequency, and amplitude of the motion.

2. What is the new equilibrium position of this mass?

3. What is the maximum speed of this mass?

4. Calculate the energy of the system…

a. when the mass is at its lowest point. b. when the mass is at the equilibrium position.

5. Graph the position, velocity, and acceleration of the mass as a function of time for the first two complete oscillations.

SIMPLE HARMONIC MOTION III – PENDULUM

1. A simple pendulum 4 m long swings with an amplitude of 0.20 m.

a. Compute the period and frequency of the pendulum.

b. Compute the linear velocity at its lowest point.

c. Compute the linear acceleration of the pendulum at either end of its path.

d. If the pendulum is shortened to a length of 2.0 m, what happens to your answers in (a), (b), and (c)?

2. A certain pendulum has a period on Earth of 2.0 seconds. What is the period on the moon, where the acceleration due to gravity is roughly 1/6th of its value on Earth?

3. A grandfather clock, which keeps time on Earth by means of a simple pendulum, is taken to the moon.

a. If the clock is operated on the moon in the same fashion, will the clock run slow or fast?

b. How much time passes on Earth while the hands of the grandfather clock on the moon move through 24 hours?

Due Date:
February 3rd at 11:59 pm[1] / Student Name:
Course Name: AP Physics
Period: 3
Teacher Name: Mr. Khalilian
Assignment Title: / End of Unit Lab: Hooke’s Law and Simple Harmonic Motion for Elastic Materials
Assignment Summary: / Your job is to use simple harmonic motion to create a claim which answers the following question:
What are the spring constants for a given rubber band and spring?
You will have 2 class days. The recommended course of action is:
· Decide how you want to create your collisions and what measuring devices you want.
· Make measurements using your collisions and decide how to account for experimental error.
· Create your claim.
Format: 5 – 10 deductions possible for any infraction / · MLA Format heading
· Title: The SHM Lab Write-Up
· Submitted to Turnitin.com. (Without this, the lab report is a 0.) / · Section headers for each section from the rubric.
· You do NOT need to submit a paper copy.
Procedure and Helpful Hints: / Before writing your paper, you should:
1. Determine what measurements need to be taken.
2. Take the necessary measurements.
3. Write the lab report, carefully.

SHM PRACTICE AND REVIEW

1. A mass m is attached to a spring with a spring constant k. If the mass is set into simple harmonic motion by a displacement d from its equilibrium position, what would be the speed, v, of the mass when it returns to the equilibrium position?

Questions 2-3: A block oscillates without friction on the end of a spring as shown. The minimum and maximum lengths of the spring as it oscillates are, respectively, xmin and xmax. The graphs below can represent quantities associated with the oscillation as functions of the length x of the spring.

(A) (B) (C) (D)

2. Which graph can represent the total mechanical energy of the blockspring system as a function of x ?
(A) A (B) B (C) C (D) D

3. Which graph can represent the kinetic energy of the block as a function of x ?
(A) A (B) B (C) C (D) D

4. An object is attached to a spring and oscillates with amplitude A and period T, as represented on the graph. The nature of the velocity v and acceleration a of the object at time T/4 is best represented by which of the following?

(A) v > 0, a > 0 (B) v > 0, a < 0

Questions 5-6

A sphere of mass m1, which is attached to a spring, is displaced downward from its equilibrium position as shown above left and released from rest. A sphere of mass m2, which is suspended from a string of length L, is displaced to the right as shown above right and released from rest so that it swings as a simple pendulum with small amplitude. Assume that both spheres undergo simple harmonic motion

5. Which of the following is true for both spheres?

(A) The maximum kinetic energy is attained as the sphere passes through its equilibrium position

(B) The maximum kinetic energy is attained as the sphere reaches its point of release.

(D) The maximum gravitational potential energy is attained when the sphere reaches its point of release.

(E) The maximum total energy is attained only as the sphere passes through its equilibrium position.

6. If both spheres have the same period of oscillation, which of the following is an expression for the spring constant?

(A) L / m1g

(B) g / m2L

(D) m1g / L

Question 7 refers to the graph below of the displacement x versus time t for a particle in simple harmonic motion.

7. Which of the following graphs shows the kinetic energy K of the particle as a function of time t for one cycle of motion?