1. CALIFORNIA STATE UNIVERSITY, LOS ANGELES
Department of Physics and Astronomy
Physics 212-14 / Section 14- 34514
Standing waves On Strings
Prepared by: Faustino Corona,
Noe Rodriguez,
Rodney Pujada,
Richard Lam
Performance Date: Tuesday,April 6, 2016
Submission Due: Tuesday, April 13, 2016
Professor: Ryan Andersen
Wednesday: 6:00 pm. – 8:30 p.m.
April 2016
2. Experiment No 2: Pendulums
I. ABSTRACT
To experiment the relation between wave velocity and spring’s tension by using
standing waves
II. INTRODUCTION
In this experiement we are using an electrically driven vibrartor of 60HZ frequency that is
attached to a set of weights with a weight holder.
f=frequency in cycles/second (HZ)
λ=wavelength
v=f λ, the speed of propagation of the wave in any medium
τ =tension in the string, equal to "mg" if produced by a hanging mass "m"
μ =mass per unit length of the string
VTH=, the theoretical speed of propagation of a wave along a string under tension
k=2π/λ, the wavenumber of the wave
ω =2f=kv
III. EXPERIMENTAL PROCEDURE
3. IV. DATA AND ANALYSIS
4.1. SINGLE PENDULUM : DEPENDENCE OF PERIOD ON LENGTH
DATA TABLE 1: For this part of the experiment the mass was fixed at 50 g.
L(cm) L(m) T (seconds)
No
Cycles
Period (T) T
2
(s)
10 0.1 5.43 10 0.543 0.295
20 0.2 8.56 10 0.856 0.733
40 0.4 12.26 10 1.226 1.503
80 0.8 18.03 10 1.803 3.251
120 1.2 22.49 10 2.249 5.058
160 1.6 25.82 10 2.582 6.667
DATA TABLE 2: All times are measure in seconds.
L(m) T
2
(s)
0.1 0.295
0.2 0.733
0.4 1.503
0.8 3.251
1.2 5.058
1.6 6.667
GRAPH PERIOD (T2
)VS LENGTH : The data was copied into Excel and graphed,
showing the linear regression.
Graph No 1 : Period Vs Length for simple pendulum
4. The linear equation is T2 = 4.2799L - 0.1494 with a correlation of R² = 0.9997
We have our equation T2 = (4π2
/ g) L where (4π2
/ g) is the slope in our graph.
4.2. PHYSICAL PENDULUM: PERIOD VS ANGLE
DATA TABLE 4
T/2
(seconds)
(°)ϴ Period (T)
4.65 30 9.3
4.87 60 9.74
4.99 90 9.98
5.5 120 11
6.81 150 13.62
8.66 180 17.32
Graph No 2 Period vs angle.
6. a) Measure the period for normal mode #1
OBSERVATIONS: Both masses have the same frequency and direction when they are
release. Every pendulum has a natural or resonant frequency, which is the number of times
it swings back and forth per second. The resonant frequency depends on the pendulum’s
length. Longer pendulums have lower frequencies.
b) Measure the period for normal mode #2
OBSERVATIONS: In opposite directions both masses have the same frequency.
c) Measure the period for normal mode # 3
OBSERVATIONS: Observe this “energy exchange motion”. Note that the total amount of
energy in the system remains constant, but it is constantly being passed between the two
pendula. Pendulum 2 speeds up at the expense of pendulum 1 slowing down, and vice versa.
The energy “sloshes” back and forth between the two parts of the system. The spring
provides the transfer mechanism. This simple system models the complex energy transfers
that occur in nature. We observe measure the period of energy exchange.
DATA TABLE 5: Couple Pendulums : Experiment changing the mode.
Coupled
Pendulums
T(seconds)
L (cm) Height of
connection
between
pendulum
Mode # 1 14.83 32.5
Mode # 1 14.8 13.5
Mode # 2 9.8 32.5
Mode # 2 13.16 13.5
7. Mode # 3 3.04 32.5
Mode # 3 11.65 13.5
4.4. CALCULATION OF G
Where the slope is 4.2799. Therefore 4.2799 = 4 π2 / g
Find g: 4.2799
The graph No 1 show the dependence of T2 on L, where the slope of the graph is
Since slope = 4.2799
g = (2π) 2/slope = (2π) 2
/ 4.2799
g = 9.22m/s2
g = 9.22m/s2
The error here, comparede to the expected value of g = 9.80 m/s2
is
4.5 CALCULATION OF PERCENT DIFFERENCE
We appreciate
Calculate the percent of error:
Percent error = ( Dpractical — Dtheoric) x 100 % … formula 1
Average(practical value + Theorycal value)/2
Data:
g= 9.22 m/s2
( graph No 1 (calculation from slope in the graph part 4.4)
g = 9.8 m/s2
to evaluate percent of error.
Average(practical value + Theorycal value)/2 = (9.22+ 9.80 )/2 = 9.51
Percent error = {(9.22 - 9.88) / 9.51 }x100% = -6.1 %
9.51
Percent error = -6.1 %
V. RESULTS
This experiment has three parts:
For simple pendulum, they do not dependence from angle and mass. We calculate by the
linear regression the slope of 4.2799. We can calculate a practical value 9.22 m/s2
The period vs. length measurements were well described by a power law. Using Excel to fit
the data, the best power-law fit is:
From the second part: We appreciate the physical pendulum do not depende form the angle (
graph No 2)
8. From the last part: A small error is introduced by assuming that the motion is simple
harmonic. (A real pendulum only approximates simple harmonic motion.) There is some
friction in the string where it moves on the metal rod, and there is some air friction. Also,
the theoretical value used for g may be slightly off due to local variations in its value. There
may be some error introduced by imperfections in the ruler used to measure length and in
the stopwatch. An additional error is introduced by the innate variation in human reaction
time when operating the stopwatch.
VI. CONCLUSIONS
From the results of our experiment we can observe that in the insistence of Period (Time)
vs. Length we notice that if you stretch it 10 cm or 180 cm the Period would increase as the
length increases. This dependence how much time between the Periods (T) since timing is a
big factor when doing this experiment and some slight error might occur in timing. But
when you observe the experiment, when length is no longer in account but amplitude is you
would notice the change in time would not change if surface is frictionless. If more of an
angle is add the time should be similar and reach the ten cycles we are using to observe at
the same time in this experiment. Some agreements with the predictions is that the
amplitude should not have an effect on period because at first there were close in time but
then we notice that friction in the disk was causing it to slow down and that length does
have an effect on period depending on the amount of length placed on the spring. I have to
disagree with some results since without precision some numbers would be off. For example
period because timing is an issue since we can never get the time right this is why we had to
do ten cycles to get the most precision in this experiment. Another issue was measurements
because we did not have a precise measurement technique we had to eyeball the lengths of
the strings and also if it’s close to the amplitudes we want. Meaning that in some instances
the amplitude we want to reach can be a bit over or under meaning that this can make the
error a bit more than it should. Some possible improvements are finding new ways to
measure distances more accurately and time as well.
VII. REFERENCES
• Department of Physics and Astronomy CSU Los Angeles. Edition 2.0, XanEdu
Custom Publishing, pp. 8-14
VIII. DATA SHEETS
