1. Chapter 11
Vibrations and Waves
Ms. Hanan

2. 11-2 Measuring Simple harmonic Motion
Objectives
Identify the amplitude of vibration.
Recognize the relationship between period and frequency.
Calculate the period and frequency of an object vibrating with simple harmonic motion.

3. Vocabulary Periodic Motion Simple Harmonic Motion Spring-mass system
Pendulum
Vibration
Oscillation
Cycle
Period
Amplitude
Frequency
Spring Constant

4. Amplitude, Period, and Frequency
Amplitude is the maximum displacement from equilibrium.
Period is the time it takes to execute a complete cycle of motion.
Frequency is the number of cycles or vibrations per unit of time.

5. Amplitude
Pendulum: amplitude can be measured by the angle between the pendulum’s equilibrium position and its maximum displacement.
Mass-spring system: amplitude is the maximum amount the spring is stretched or compressed from its equilibrium position.

6. Period and frequency measure time
Swinging from maximum displacement on one side of equilibrium to maximum displacement on the other side and back again = one cycle
Period (T): the time it takes for this complete cycle of motion. Units: second, s
Frequency (f): the number of complete cycles in a unit of time. Units: 1 s-1= 1 Hz

8. Period of a Simple Pendulum in Simple Harmonic Motion
Depends on string length and free-fall acceleration.
L = length

9. T = 12 s g = 9.81 m/s2 Unknown: L = ? Sample Problem B
You need to know the height of a tower, but darkness obscures the ceiling. You note that a pendulum extending from the ceiling almost touches the floor and its period is 12s. How tall is the tower?
Given:
T = 12 s g = 9.81 m/s2
Unknown:
L = ?

10. Sample Problem 12B

11. Assignments
Class-work:
Practice B , page 379, questions 1, 2, 3, and 4.
Homework:
Section review on page 381 questions 1 and 2
Review; Page 397: # 19 and 20

12. Period of a Mass-Spring System
Depends on mass and spring constant.

13. Sample Problem C
The body of a 1275 kg car is supported on a frame by four springs. Two people riding in the car have a combined mass of 153 kg. when driven over a pothole in the road, the frame vibrates with a period of s. for the first few seconds, the vibration approximates simple harmonic motion. Find the spring constant of a single spring.
Given:
T = s
Unknown:
k = ?

14. Sample Problem B

15. Assignments
Class-work:
Practice c , page 381, questions 1, 2, 3, 4, and 5.
Homework:
Section review on page 381, odd questions
Review; Page 397: # 21