19.2 Graphs of Harmonic Motion pp 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

 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 Time (s) Displacement (cm)

Graphs of Harmonic Motion: Amplitude Time (s) Displacement (cm)

Graphs of Harmonic Motion: Period Time (s) Displacement (cm) T = 4 seconds

Graphs of Harmonic Motion: Frequency Time (s) Displacement (cm) 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