Harmonic Motion

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Harmonic Motion
Harmonic & Linear Motion
Pendulum Basics
The Effect of weight on Period
The Effect of Amplitude on Period
The Effect of Length on Period
Damping
Harmonic & Linear Motion

Harmonic motion

Any motion that repeats over and over again
Examples: Swing, car tire after hitting a bump, clock
hands, heartbeat, planets orbiting, etc.
 Color and Music are both created by harmonic motion


Occurs whenever the is a restoring force

Restoring force is the force that makes the object
return to its starting point


In the pendulum, the restoring force is the part of the weight
that is not supported by the string
Linear Motion

Motion that goes from one place to another
Pendulum Basics


The length of the pendulum is
measured from the pivot point
to the middle of bob
The amplitude is how far the
pendulum is pulled from its
resting point

Amplitude can be measured in
centimeters or degrees
The Effect of Weight on the Period
of a Pendulum

Weight does not affect the period of a
pendulum

Force Explanation

Since gravity accelerates all objects at the same rate,
the pendulum accelerates the same no matter how
heavy it is.



Heavy pendulums have more inertia (are harder to move),
but gravity pulls harder on heavier objects.
The larger force of gravity is canceled by the object’s inertia,
so the pendulum travels at the same rate
Energy Explanation

We know that the speed of a falling object is given by
v=√2gh. Mass doesn’t matter
Comprehension Check

If we took a pendulum to the moon, what
would happen to its period and its
amplitude?


The smaller force of gravity would cause the
pendulum to accelerate more slowly, increasing
the period. The amplitude would remain the
same as on Earth.
What if we took the pendulum to Neptune,
which is about 16 times bigger than Earth?

The increase in gravity would make the
pendulum accelerate 16 times faster, decreasing
the period dramatically. The amplitude would
remain the same as on Earth.
The Effect of Amplitude on the
Period of a Pendulum

Amplitude does not affect the period

Force Explanation

A bob with a greater amplitude has a larger distance
to travel, but it is going faster than a bob with small
amplitude


At a higher amplitude, less of the bob’s weight (force of
gravity) is supported by the string so more force is available
to accelerate the bob.
Energy Explanation

At a higher angle the bob has more potential energy
to transfer into kinetic energy, meaning that it will be
traveling faster when it reaches the bottom of the
swing.
Comprehension Check

James made a pendulum by hanging a 1N and 3N
weight from the same string. James measured 5
periods to be 7.5 seconds. He swung the
pendulum again but this time the 1N weight fell off
at the bottom of the second swing. How long did it
take the pendulum to finish 5 period this time?


The pendulum’s period would not be affected by the loss
of the weight.
Michelle swings a pendulum and measures the
period to be 5.0s. She then leaves the room for a
couple hours and returns to find the pendulum
barely swinging. She again times the period. How
should the new period compare to the old one?

Since the amplitude does not affect the period, both
periods should be exactly the same.
The Effect of Pendulum Length on
the Period

As the length of a pendulum increases the
period also increases

Force Explanation


The longer pendulum has a longer distance to travel,
but doesn’t travel much faster. This results in a
longer period.
Energy Explanation
The longer pendulum has to be lifted higher and has
more potential energy to convert to kinetic energy
 The greater speed, however, is not enough to make
up for the greater distance traveled.

Comprehension Check

Jill has a grandfather clock that keeps track of time
by counting the swings of a pendulum. If her clock
is running slow, what should she do to the
pendulum to fix the problem?


Jill needs to speed up the pendulum, which means she
needs to make the pendulum shorter.
Tracey, an eight year old girl is racing her bigger
brother on a swing. Even though the swings are
the same length, he always beats her no matter
how hard she pumps her legs. Can you explain
why the bigger brother always wins?
Damping

Damping – The gradual loss of energy and
amplitude

The friction results from wind resistance and
the friction between the rope and stand


Gravity keeps the pendulum going, its damping
that makes it stop eventually


The friction converts some the energy into heat
Without friction, the pendulum would swing forever
Damping only affects the amplitude

Since amplitude does not affect the period, damping
does not affect the period
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