Today’s Topic: Simple Harmonic Motion Explanation

Learning Goal:

SWBAT name the parts of a wave, and explain the relationship between frequency

and period.Describe the similarities that exist between

these two objects.

Both are undergoing Simple Harmonic Motion!

Homework

Complete the Pendulum Lab (Due Thursday, May 28th).

Complete the Simple Harmonic Motion Worksheet. (Due Thursday, May 28th)

VibrationAll things around us are constantly

wiggling and jiggling in place.

However, most of these objects aretoo small to see.

What are some objects that are currently wiggling and jiggling in this room?

VibrationObjects in their natural state of rest are

in their equilibrium position.

When objects move back and forth from their equilibrium position, they are said to be vibrating.

VibrationVibrations need time in order to move

back and forth, or oscillate.

The pendulum we see up here, as well as the spring-mass system are examples of objects that move in simple harmonic motion.

The true definition of simple harmonic motion is a bit unwieldy, but here it is:

VibrationSimple harmonic motion is a type of

periodic motion where the force acting on the object is directly proportional to the displacement and acts in the direction opposite of displacement.

Let’s pick this apart with the spring-mass.

For all intents and purposes, think of the pendulum and spring-mass system here.

Period

The time it takes for an oscillating object to complete one full cycle is its period.

In Physics, period is written as T, and is measured in seconds.

Think of T as the TIME it takes tocomplete one full oscillation.

Period of a PendulumWhat did our lab from yesterday tell us

about the period of a pendulum?

Period of a pendulum only depends on:The length of the pendulumThe acceleration due to gravity

Tpendulum = 2π

Tpendulum = 2π

Example Problem

What is the period of a pendulum on Earth with a length of 70 cm?

If this same pendulum were brought to Io, one of the moons of Jupiter where the acceleration due to gravity is 1.796 m/s2, how much longer would the period be?

Answer: 1.679 s

Answer: 2.244 s

Period of a Pendulum

Galileo Galilei was the first to observe and discover this fact – the mass of a pendulum has no effect on its period.

Period of a PendulumMIT’s Walter Lewin demonstrated this

discovery as well in one of his classes.

Here, he compares the time it takes for 10 pendulum oscillations with and without extra mass.

More S.H.M.The mass and spring also exhibit simple

harmonic motion.

The period of the mass and spring system depends only on:The mass at the end of the spring

The spring constant of the spring

More S.H.M.This formula may be written as:

Tmass-spring = 2π

Tmass-spring = 2π

Example Problem

A mass-spring system oscillates with a period of 0.45 seconds. What is the spring constant of the spring if the mass is 625 grams?

Answer: 121.847 N/m

Period and Its InverseA 6.2 cm long pendulum oscillates very

quickly. What is the period of this pendulum?

So how many seconds does it take per swing?

What if we wanted to know how many swings it can make per second?

Answer: 0.5 s

Period and Its InverseFlip that upside-down!

The period tells us how many seconds it takes for one complete cycle to occur.

If we wanted to know how many cycles occur in one second, we would be asking for its frequency.

FrequencyThe formula for frequency is:

f =

frequency =

[Hz][s]

1f T

FrequencyThe units for frequency are the Hertz.

They are named after the German scientist Heinrich Hertz – who did extensive work in the field of electromagnetism, as well as radio transmission.He was the first to conclusively prove the

existence of electromagnetic waves.

FrequencyTechnically, a Hertz is a s-1, or So the pendulum we found has “a

frequency of 2 Hz.”

Fun Fact:

FM Radio stations broadcast their signals in the MHz range. What does M mean?

When I listen to NPR on 93.9 FM, what is the frequency that my radio is picking up?