19.2 Graphs of Harmonic Motionpp. 419 - 422

Mr. Richter

Agenda

Warm Up

Review HW

Recap Period and Frequency

Graphs of Harmonic Motion

Objectives: We Will Be Able To…

Draw and interpret graphs of harmonic motion.

Determine amplitude, period and frequency from a harmonic motion graph.

Warm-Up: Recap

A vibrating string moves back and forth 20 times in 8 seconds.

1. Does it take longer than one second for one complete cycle?

2. What is its period?

3. What is its frequency?

Recap Period and Frequency

Period and Frequency

The period (T) of an object’s motion is the time it takes for an object to complete one full cycle of motion. Because period is a measurement of time per cycle, the

units of period (T) are units of time: seconds.

The frequency (ƒ) of an object’s motion the number of cycles the object completes per unit of time.

Frequency is a measure of how many cycles per unit time, so the units of frequency are “per seconds” We abbreviate as Hertz (Hz).

Period and Frequency

You may have noticed that period and frequency are inverses of each other.

If an object takes 8 seconds to complete 20 cycles: It completes 1 cycle in 8/20 seconds (T = 0.4 seconds) It completes 20/8 cycles per second (ƒ = 2.5 Hz)

Graphs of Harmonic Motion

Graphs of Harmonic Motion

An example:

Let’s say there is a pendulum that takes 4 seconds to complete a cycle, and it oscillates back and forth from –10 cm to 10 cm.

What does that graph look like? Let’s plot some points.

Graphs of Harmonic Motion

10

-10

Time (s)

1 2 3 4 5 6 7 8

Dis

pla

cem

ent

(cm

)

Graphs of Harmonic Motion: Amplitude

10

-10

Time (s)

1 2 3 4 5 6 7 8

Dis

pla

cem

ent

(cm

)

Amplitude = 10 cm

Amplitude = 10 cm

Graphs of Harmonic Motion: Period

10

-10

Time (s)

1 2 3 4 5 6 7 8

Dis

pla

cem

ent

(cm

)

T = 4 seconds

T = 4 seconds

T = 4 seconds

Graphs of Harmonic Motion: Frequency

10

-10

Time (s)

1 2 3 4 5 6 7 8

Dis

pla

cem

ent

(cm

)

T = 4 seconds

T = 4 seconds

T = 4 seconds

Wrap-Up: Did we meet our objectives?

Draw and interpret graphs of harmonic motion.

Determine amplitude, period and frequency from a harmonic motion graph.

Homework

p. 431 Solving Problems

# 1, 2, 4, 6, 7