Chapter 11Chapter 11

Vibrations and Waves

Ms. Hanan

11-2 Measuring Simple harmonic 11-2 Measuring Simple harmonic MotionMotion

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.

VocabularyVocabulary

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

Amplitude, Period, and FrequencyAmplitude, 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.

AmplitudeAmplitude

• 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.

Period and frequency measure timePeriod 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

Period of a Simple Pendulum in Simple Period of a Simple Pendulum in Simple Harmonic MotionHarmonic Motion

Depends on string length and free-fall acceleration.

L = length

Sample Problem BSample 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 = ?

Sample Problem 12BSample Problem 12B

mL

Ls

Ls

Ls

g

L

sm

sm

sm

364

81.9144

81.9

4144

81.9212

2 T

2

2

22

2

2

2

AssignmentsAssignments

• 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

Period of a Mass-Spring SystemPeriod of a Mass-Spring System

Depends on mass and spring constant.

Sample Problem CSample 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 0.840 s. for the first few seconds, the vibration approximates simple harmonic motion. Find the spring constant of a single spring.

Given:

T = 0.840 sUnknown:

k = ?

357kg

4153kg1275kg

m

Sample Problem BSample Problem B

mNk

s

kg

T

mk

k

mT

k

m

/1000.2

840.0

35744

4

2 T

4

2

2

2

2

22

AssignmentsAssignments

• 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