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EXAS
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NSTRUMENTS
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ETTING
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TARTED WITH
CBR
21
Activity 3—Pendulum
notes for teachers
Concepts
Function explored: sinusoidal.
Explore simple harmonic motion by observing a free-
swinging pendulum.
Materials
Ÿ
calculator
Ÿ
CBR
Ÿ
calculator-to-CBR cable
Ÿ
mounting clamp
Ÿ
stopwatch
Ÿ
pendulum
Ÿ
meter stick
Ÿ
TI ViewScreen (optional)
Ideas for weights:
0
balls of different sizes (
≥
2" diameter)
0
soda cans (empty and filled)
0
bean bags
Hints
See pages 6–12 for hints on effective data collection.
Physical connections
An object that undergoes periodic motion resulting
from a restoring force proportional to its displacement
from its equilibrium (rest) position is said to exhibit
simple harmonic motion (SHM). SHM can be described
by two quantities.
0
The period
T
is the time for one complete cycle.
0
The amplitude
A
is the maximum displacement of
the object from its
equilibrium position
(the position
of the weight when at rest).
For a simple pendulum, the period
T
is given by:
T
= 2
p
L
g
where
L
is the string length and
g
is the magnitude of
the acceleration due to gravity.
T
does not depend on
the mass of the object or the amplitude of its motion
(for small angles).
The frequency
f
(number of complete cycles per
second) can be found from:
f =
1
T
, where
f
is in hertz (Hz) when
T
is in seconds.
The derivatives of a sinusoidal plot are also sinusoidal.
Note particularly the phase relationship between the
weight’s position and velocity.
Typical plots
Typical answers
1. varies (in meters)
2. varies (in meters)
3. varies (in seconds);
T
(one period) = total time of
10 periods
à
10; averaging over a larger sample
tends to minimize inherent measurement errors
4. the total arc length, which should be
approximately 4 times the answer to question 2;
because an arc is longer than a straight line
5. sinusoidal, repetitive, periodic; distance from the x-
axis to the equilibrium position
6. each cycle is spread out horizontally; a plot
spanning 10 seconds must fit more cycles in same
amount of screen space, therefore cycles appear
closer together
7. (total # of cycles)
à
(5 seconds) = cycles
à
second;
easier to view full cycles, and fewer measurement
errors
8.
f
= 1
à
T
, where
T
is time for 1 period
9. decreased period; increased period
(Pendulum length is directly related to period time;
the longer the string, the longer the period.
Students can explore this relationship using the
calculator’s list editor, where they can calculate the
period for various values of
L
.)
10.
A
(amplitude) = ¼ total distance that the
pendulum travels in 1 period
11. both sinusoidal; differences are in amplitude and
phase
12. equilibrium position
13. when position = maximum or minimum value
(when the weight is at greatest distance from
equilibrium).
14. It doesn’t.
T
depends only on
L
and
g
, not mass.
Advanced explorations
Data collection: the plot of L2 versus L3 forms an
ellipse.
