C
OPYING PERMITTED PROVIDED
TI
COPYRIGHT NOTICE IS INCLUDED
© T
EXAS
I
NSTRUMENTS
I
NCORPORATED
G
ETTING
S
TARTED WITH
CBR
23
Activity 3—Pendulum
(cont.)
sinusoidal
Explorations
Data collection 2
From the
MAIN MENU
choose
SETUP
à
SAMPLE
. On the
SETUP
screen, change the time from 10
to 5 seconds. Repeat the data collection. Observe the plot.
Answer questions 6 and 7.
The quantity you determined (cycles per second) is called the
frequency
. Although you
calculated frequency in question 7 using the plot, you can find it mathematically from:
f =
1
T
where
T
is the period in seconds, and
f
is the frequency in hertz (Hz).
Answer question 8.
Data collections 3 and 4
Repeat the 5-second data collection two more times. First, shorten the string. Second,
lengthen the string. After observing those plots,
answer question 9
.
Another important distance measurement affecting the motion of the pendulum is the
amplitude
. The answer to question 2 was the amplitude of that pendulum swing.
Answer
question 10.
Advanced explorations
Data collection 5
From the
PLOT MENU
choose
VELOCITY-TIME
.
Answer questions 11, 12 and 13.
Data collection 6
Repeat the data collection with a significantly lighter or heavier weight, and then
answer
question 14.
Model the distance-time behavior of the pendulum using the form for a sinusoidal function,
S = A sin (wt +
d
)
, where
S
is the instantaneous position,
A
is the amplitude,
w
is the
frequency,
d
is the phase angle, and
t
is the time. The frequency,
w
, is related to the period,
T
, by
w = 2
p à
T .
Enter this equation in the Y= editor using the calculated values of
A
and
w
. Simultaneously
graph this function and the statistical plot of
L1
(time) versus
L2
(distance). Adjust the values
of
A
,
w
, and
d
until a good fit is obtained. On the TI
-
83 or TI
-
86, use the sine regression to
determine the values.
Explore the relationship between position and velocity by plotting
L2
(distance) versus
L3
(velocity). What do you predict for the appearance of the resulting plot? Compare the actual
result to your prediction.