Lab report
Pendulum
Objective – in this lab we will study about the simple pendulum and we will also study how the time period change with length, mass and initial displacement of pendulum.
Instruments – PHET simulation
Theory –
Time period of simple pendulum depends on the
So time period depends on the length of pendulum and gravitational acceleration at that place, so it is independent of mass, initial displacement.
Procedure –
(1) Open the PHET simulation and go to the lab section. Click on the stopwatch box.
(2) Give the initial deflection of 25 degree.
(3) Record the time for 10 oscillations. Do same, 4 more times with same deflection and record the time.
(4) Take the average of the five observations and find the time period for one oscillation and standard deviation in the observations.
(5) Repeat step (2) and (3) for 30, 35, 40, 45 degree deflection.
(6) Now set the initial deflection at 30 degree and repeat step (3) , (4) for length 0.8m, 0.6m, 0.4m, 0.2m.
(7) Similarly repeat step (3) and (4) for mass 0.25 kg, 0.5 kg, 0.75kg , 1.00 kg.
Observations –
Table (1)
angle
time for 10 oss
t1
t2
t3
t4
t5
avg
stdev
T
30
20.48
20.29
20.34
20.41
20.34
20.372
XXXXXXXXXX
2.0372
Table (2)
angle
time for 10 oss
t1
t2
t3
t4
t5
avg
stdev
T
25
20.39
20.5
20.45
20.31
20.37
20.404
XXXXXXXXXX
2.0404
35
20.3
20.32
20.77
20.56
20.49
20.488
XXXXXXXXXX
2.0488
40
20.4
20.58
20.6
20.54
20.66
20.556
XXXXXXXXXX
2.0556
45
20.8
20.78
20.65
20.88
20.69
20.76
XXXXXXXXXX
2.076
Table (3)
length
time for 10 oss
t1
t2
t3
t4
t5
avg
stdev
T
0.8
18.39
18.42
18.39
18.57
18.44
18.442
XXXXXXXXXX
1.8442
0.6
15.82
15.89
15.84
15.77
15.92
15.848
XXXXXXXXXX
1.5848
0.4
13.05
12.94
13.09
13.1
12.91
13.018
XXXXXXXXXX
1.3018
0.2
9.1
9.17
9.06
9.22
9.15
9.14
XXXXXXXXXX
0.914
Table (4)
mass
time for 10 oss
t1
t2
t3
t4
t5
avg
stdev
T
0.25
20.44
20.56
20.67
20.34
20.76
20.554
XXXXXXXXXX
2.0554
0.5
20.32
20.37
20.48
20.65
20.34
20.432
XXXXXXXXXX
2.0432
0.75
20.4
20.44
20.67
20.26
20.54
20.462
XXXXXXXXXX
2.0462
1
20.6
20.38
20.49
20.39
20.28
20.428
XXXXXXXXXX
2.0428
Calculation –
For table (1)
L = 1m
G = 9.81
Standard deviation -
Average time = XXXXXXXXXXsec
standard deviation
average
20.372
diff
Square of difference
Values t1
20.48
0.108
XXXXXXXXXX
T2
20.29
0.082
XXXXXXXXXX
T3
20.34
0.032
XXXXXXXXXX
T4
20.41
0.038
XXXXXXXXXX
T5
20.34
0.032
XXXXXXXXXX
average
XXXXXXXXXX
root of average
XXXXXXXXXX
Standard deviation = 0.07
Data Analysis
1. What is the uncertainty for your measurements of period ??
Uncertainity XXXXXXXXXX
2. How does measuring the period for 10 cycles affect your uncertainty in the measurement of one period?
As we increase the number of observations it will decrease the uncertainty in observations.
3. Why did we use the standard deviation from multiple measurements as our estimate of uncertainty?
Because our distribution is normal and we are taking the deviation form the average value of observation.
4. Using a graph, determine the relationship between length and period. An Excel spreadsheet or Google Sheets document to create a graph is the best way to do this.
If we plot a graph between the square of time period and length then it will be a straight line.
a. Does the period depend on length? If so, how?
Yes time period depends on the length
T α sqrt(L) …………….(A)
. Is this what you expected?
yes
5. using a graph, determine the relationship between initial angle and period.
a. Does the period depend on initial angle? If so, how?
We see that as we increase the angle time period also increase.
. Is this what you expected?
No.
6. Using a graph, determine the relationship between mass and period.
a. Does the period depend on mass? If so, how?
No
. Is this what you expected?
yes
7. Using the appropriate data set, calculate the value of ?, the acceleration owing to gravity. Comment on your value. Is it what you expected?
We plot the graph between the length and time period by using the table (2) data.
Slope of this graph
So
Actual value = 9.81
Percentage difference =
So that is expected answer.
Conclusion -
We have studied about the simple pendulum and how it behaves in changing the length, mass, and initial displacement.
We found that it depends on the length only(equation A). Observations show that it also depends on the initial displacement but that is due to measurement e
or in time.
Te graph between the T^2 and L is a straight line which matched with theory. We have also found the experimental value of g which is 9.339 m/s^2 with 4.8 % e
or form the theoretical value, so this e
or is inacceptable range.
Graph between the L and T^2
0.8 XXXXXXXXXX 0.4 0.2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX lenght (m)
T^2 sec^2
graph between the iniital angle and tim period
25 35 40 45 XXXXXXXXXX 2.0488 XXXXXXXXXX XXXXXXXXXX angle (degree)
time period (s)
Graph between the mass and time period
0.25 0.5 XXXXXXXXXX 1 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX Mass (kg)
Time period(s)
Graph between the L and T^2
0.8 XXXXXXXXXX 0.4 0.2 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX lenght (m)
T^2 sec^2
University of Hartford PHY113 Fall 2020
Waves on a String
General Information
Purpose
In this lab you will observe standing waves on a string and study the conditions that are
equired for their creation.
Resources Needed
Introductory Video: https:
ensemble.hartford.edu/Watch/He45Xmp6
Simulation Page:
https:
phet.colorado.edu/sims/html/wave-on-a-string/latest/wave-on-a-string_en.html
Theoretical Background
If a string is stretched tight and fixed at both ends, a wave pulse can be sent down the string,
where it will be reflected and inverted at the far end. If a second wave pulse is sent down the
string, it will combine with the reflected wave according to the principle of superposition. If a
series of wave pulses are sent down the string, standing waves can form (see Figure 1).
Standing waves are characterized by the presence of nodes, points of no vi
ation, and
antinodes, points of maximum vi
ation, which are located at fixed locations on the string.
Figure 1: Photo by OpenStax is licensed under CC BY 4.0
The distance between two adjacent nodes will be called a loop. Each loop is one half a
wavelength, ??/2. It can be seen from the figure that standing waves can only occur when an
integer number of loops can fit in the total distance ??. Assuming a source of fixed frequency ??,
how can we manipulate the conditions to ensure standing waves? For waves, the velocity of
propagation of the wave is related to its frequency and wavelength by the basic wave relation
https:
ensemble.hartford.edu/Watch/He45Xmp6
https:
phet.colorado.edu/sims/html/wave-on-a-string/latest/wave-on-a-string_en.html
https:
openstax.org
ooks/university-physics-volume-1/pages/16-6-standing-waves-and-resonance
https:
openstax.org
https:
creativecommons.org/licenses
y/4.0
University of Hartford PHY113 Fall 2020
?? = ???? (3.1)
The speed of a wave on the string should be affected by the type of string (its cross section,
weight, etc.). It is observed that waves travel more slowly down a thicker string, a quality that
can be characterized by the linear density, ??.
?? =
??
??
(3.2)
It is also observed that waves travel faster down a tighter string, thus the tension (a force) ?? is a
factor. The speed of the wave will be
?? = �
??
??
(3.3)
By comparing equations 3.1 and 3.3, we can see that the properties of the wave are dependent
on the properties of the medium, in this case the string.
???? = �
??
??
(3.4)
Experimental Procedure
1. Bring up the simulation and familiarize yourself with the controls. In particular, note that
the reset button on the bottom right will return all the settings to the default values while
the restart button at the top left will begin with a fresh simulation with whatever changes
you have made and leave any other values unchanged.
2. Add rulers to the simulation and record the length of the string from the center of the green
all at the oscillator to the green ball in the clamp.
3. Finding the Effect of Damping
Use the following settings:
Amplitude Pulse Width Damping Tension End
1.25 cm 0.30 s First line High Fixed End
4. On the top left choose Pulse. Send a single pulse down the string. On your worksheet,
describe what happened to the wave when it was reflected.
5. Hit pause on the simulation. Add the timer and hit restart. With the simulation still paused,
hit the start button on the timer. When you send a pulse (by pushing the green button) the
timer should start automatically. Send a pulse down the string and top the timer when you
can no longer see any movement of the string. Record the time.
University of Hartford PHY113 Fall 2020
6. Repeat the timing measurement with the damping set on the second, third, fourth and fifth
lines. Make a graph of the time vs. setting (with time on the y axis). Is the damping linear?
7. Finding the Wavelength:
Reset the simulation. Set the wave generator to oscillate and use the following settings:
Amplitude Frequency Damping Tension End
1.25 cm 0.75 Hz None Medium Fixed End
8. Start the simulation and observe