Transcript 01 Notes S.H.M - McKinney ISD Staff Sites

Happy Thursday! 2-11-16
Get ready for warm up #9
Warm ups are due tomorrow!
Get ready to take notes: we are starting
on a new unit!!
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Warm up # 8
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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
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Vibrating
Tuning fork
A mass on
a spring
200
grams
A boy on
a swing
L
T  2
g
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SHM
T= period of time
L= length of pendulum
g = acceleration due to
gravity
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FORMULA FOR THE PERIOD OF A
A SPRING
Period of spring
oscillation
m
T  2
k
The “spring Constant”
is the strength of the
spring
Unit is N/m or
Newton/meter
where
m = mass
k = spring constant
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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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Small masses vibrate with
shorter periods
Large masses vibrate with
longer periods
Springs with larger constants
(stronger)
vibrate with shorter periods
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Springs with smaller
constants
(weaker)
vibrate with longer periods
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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
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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?
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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
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or
1
f 
T
SHM
Hz = sec
-1
1
= sec
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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
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SHM
Example: pendulum
PhET
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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
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where
L = length of pendulum
g = accel. due to gravity
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Definitions: Vibrations & Waves
Simple (middle school) definitions are:
Vibration – “a wiggle in time”
Wave – “a wiggle in space and time”
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