Transcript Slide 1


11.1 Simple Harmonic Motion

Periodic oscillations

Restoring Force: F = -kx



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Force and acceleration are not
constant
Amplitude (A) is maximum
displacement
Frequency is
f 
1
T
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11.1 Simple Harmonic Motion

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The system is in equilibrium is when ΣF = mg - kxo
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11.2 Energy in the Simple Harmonic Oscillator

Combination of KE and PE
1 2 1 2
E  mv  kx
2
2
1
2

When v = 0 then E  kA 2

Since energy is conserved then
k
v
( A2  x 2 )
m
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11.3 Sinusoidal Nature of Simple Harmonic Motion
Compare uniform circular motion
to the motion on a spring.

vmax
2A

T
m
T  2
k
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11.3 Sinusoidal Nature of Simple Harmonic Motion
2π t
x  A cos( ω t)  A cos(
)
T
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
11.3 Sinusoidal Nature of Simple Harmonic Motion
xmax  A
vmax
k
A
m
k
amax  A
m
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11.4 The Simple Pendulum

The restoring force is
due to gravity
F  m g sin 

If the angles are small
then
 mg
F  
x
 L 
L
T  2
g
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11.5 Damped Harmonic Motion
Tuned Mass Damper
Seismic Spring Dampers


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In class: Problems 3, 14
Other problems ↓
4. (a)
k
F
x

mg
x

 2.7 kg   9.80 m s
2
3.6 10 m
2
  735 N m  7.4 10
2
N
(b) The amplitude is the distance pulled down from equilibrium
A = 0.025 m
The frequency of oscillation is found from the total mass and
the spring constant.
f 
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1
k
2
m

1
735 N m
2
2.7 kg
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 2.626 Hz  2.6 H
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