Happy Thursday! 2-11-16
Get ready for warm up #9
Warm ups are due tomorrow!
Pick up the paper on the front table and
grab a calculator
Get ready to take notes: we are starting
on a new unit!!
REP: 2007-Nov-28
SHM
1
A box slides along the frictionless surface shown in the
figure. It is released from rest at the position shown. Is the
highest point the box reaches on the other side at level a, at
level b, or level c?
A. At level a
B. At level b
C. At level c
A box slides along the frictionless surface shown in the
figure. It is released from rest at the position shown. Is the
highest point the box reaches on the other side at level a, at
level b, or level c?
A. At level a
B. At level b
C. At level c
Simple Harmonic Motion
“back & forth”
Simple Harmonic Motion (SHM)
 simple harmonic motion – Simple harmonic motion
(SHM) is a repeated motion of a particular frequency
and period
 Happens in spring, pendulums and waves
 Occurs when the restoring force on an object is directly
proportional to the displacement of the object from its
equilibrium position
Restoring force  brings an object back to its equilibrium position
If simple harmonic motion is occurring, there are
oscillations
 Oscillations
REP: 2007-Nov-28
SHM
5
Vibrating
Tuning fork
A mass on
a spring
200
grams
A boy on
a swing
What is a pendulum?
A mass hung from a string tied at one end to a
pivot point
is free to swing down by gravity and then out
and up because of its inertia, or tendency to
stay in motion
The forces of gravity act on the pendulum to
restore it to it’s
equilibrium position
REP: 2007-Nov-28
SHM
7
Pendulum examples
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SHM
8
What is the period of a pendulum?
The period of a pendulum is the time it
takes the pendulum to make one full
back-and-forth swing.
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SHM
9
Factors that effect the period of a
pendulum
Length of the string
Starting angle (height) of the pendulum
Mass DOES NOT effect the period of a
pendulum
foucault pendulum
conservation of energy
REP: 2007-Nov-28
SHM
10
Formula for the period of a pendulum
L
T  2
g
REP: 2007-Nov-28
SHM
T= period of time
L= length of pendulum
g = acceleration due to
gravity
11
FORMULA FOR THE PERIOD OF A
A SPRING
The “spring Constant”
is the strength of the
spring
Unit is N/m or
Newton/meter
Period of spring
oscillation
m
T  2
k
where
m = mass
k = spring constant
REP: 2007-Nov-28
SHM
12
The period of oscillation of a spring
Depends upon two things:
1. The mass
2. The strength of the spring (k)
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SHM
13
Small masses vibrate with
shorter periods
Large masses vibrate with
longer periods
Springs with larger constants
(stronger)
vibrate with shorter periods
REP: 2007-Nov-28
SHM
Springs with smaller
constants
(weaker)
vibrate with longer periods
14
Spring Oscillation
You can determine the strength of a
spring, the amount of mass and the
displacement of a spring by using Hooke’s
Law
Hooke’s Law
F  kx
where
x = D length
kSHM spring constant
15
A butcher prepares cuts of meat daily. He
places a 2.2 kg package on his scale,
which compresses the scale by 2.8 cm.
What is the spring constant of his scale?
REP: 2007-Nov-28
SHM
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SHM: Period & Frequency
 Period ( T )
[measured in seconds]
 The time it takes for one complete oscillation (e.g., back-and-forth)
 Frequency ( f ) [measured in hertz (Hz)]
 The number of oscillations that occur in one second
Period & frequency are reciprocals (inverses) of each other
1
T
f
REP: 2007-Nov-28
or
1
f 
T
SHM
Hz = sec
-1
1
= sec
17
SHM: Pendulum
 Pendulums display simple harmonic motion if
the angle of displacement is small
for  small
Period of a pendulum

L
T  2
g
L
Velocity
where
L = length of pendulum
Restoring force
Equilibrium position
REP: 2007-Nov-28
SHM
Example: pendulum
PhET
18
Summary: Simple Harmonic Motion
Hooke’s Law
F  kx
Period of spring
oscillator
where
x = displacement
k  spring constant
Period of a pendulum
m
T  2
k
where
m = mass
k = spring constant
REP: 2007-Nov-28
where
L = length of pendulum
g = accel. due to gravity
SHM
19
Definitions: Vibrations & Waves
Simple (middle school) definitions are:
Vibration – “a wiggle in time”
Wave – “a wiggle in space and time”
REP: 2007-Nov-28
SHM
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