³ Activity 3 - Pendulum; Activity 3 - Pendulum Sinusoidal - Texas Instruments CBR User Manual

Activity 3—Pendulum
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:
balls of different sizes ( 2" diameter)
0
soda cans (empty and filled)
0
bean bags
0
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.
The period T is the time for one complete cycle.
0
The amplitude A is the maximum displacement of
0
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 = 2p
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:
1
, where f is in hertz (Hz) when T is in seconds.
f =
T
The derivatives of a sinusoidal plot are also sinusoidal.
Note particularly the phase relationship between the
weight's position and velocity.
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notes for teachers
Typical plots
Typical answers
1. varies (in meters)
2. varies (in meters)
3. varies (in seconds); T (one period) = total time of
10 periodsà10; 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) = cyclesàsecond;
easier to view full cycles, and fewer measurement
errors
8. f = 1àT, 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.
G S CBR
ETTING TARTED WITH
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