cceleration in One Dimension
PHYS 0212 Oscillatory Motion
1
Oscillatory Motion
This experiment has four parts:
3. Determine spring constant
k
for an inertial balance
2. Determine
g
using a simple pendulum (2 different bobs)
4. Study the pendulum motion of your arms and legs as you walk
Photogate
→
Works like a TV or DVD
remote control.
The computer
records the times when the gate is
blocked and unblocked.
Picket Fence
→
Used to measure
acceleration with one photogate.
1. Determine
g
using a photogate and picket fence
∆
x
∆
x
∆
x
∆
x
∆
x
∆
x
∆
x
∆
x
PHYS 0212 Oscillatory Motion
2
Photogate
Acceleration of a Free Falling Body
(
)
1
1
1
2
n
n
n
n
n
v
v
a
T
T
+
+
−
=
+
,
,
PHYS 0212 Oscillatory Motion
3
The Simple Pendulum
L
L
mg
x
bob
θ
We can determine the motion of the simple pendulum by
looking at the torque acting on the center of mass.
Fx
τ
=
∑
F
mg
= −
sin
x
L
θ
=
(
)(
)
sin
sin
mg
L
mgL
τ
θ
θ
= −
= −
∑
The lever arm:
sin
mgL
τ
θ
= −
∑
PHYS 0212 Oscillatory Motion
4
Displacement
cos
A
t
L
L
ω
θ
=
=
The Small Angle Approximation
If an angle is measured in radians and it is very small then we can use the small
angle approximation:
You can try this on your calculator.
Set the mode to “radians”
(rad) and take the sine of 0.1.
The answer should be 0.0998,
which is very close to 0.1.
sin
θ
θ
≈
Difference
1%
for
14
θ
≤
≤
°
sin
mgL
mgL
τ
θ
θ
= −
= −
∑
Now we can write the torque as:
Note that for Simple Harmonic Motion:
cos
A
mgL
mgL
t
L
τ
θ
ω
= −
= −
∑
(
)
cos
mg
A
t
τ
ω
= −
∑
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cceleration in One Dimension
PHYS 0212 Oscillatory Motion
5
I
τ
α
=
∑
2
cos
a
A
t
L
L
ω
ω
α
−
=
=
2
2
cos
cos
A
t
I
I
A
t
L
L
ω
ω
ω
τ
ω
−
−
=
=
∑
(
)
2
cos
I
A
t
L
ω
τ
ω
= −
∑
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 Spring '08
 Naples
 Physics, Inertia, Simple Harmonic Motion, International Space Station, oscillatory motion

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