Introduction
The following lab report is about calculating the
period of a pendulum. A pendulum is a weight suspended from a pivot so that it can swing freely. A pendulum is an example of Simple Harmonic Motion, which is periodic motion caused by a restoring force that tends to return the system to its equilibrium position.
Using the pendulum, we are going calculate the changes in its period, the time taken for one full oscillation, by changing the length of the pendulum´s arm, the mass of the object, and the amplitude.
The period of a simple gravity pendulum depends on its length, the local strength of gravity, and to a small extent on the maximum angle. It is independent of the mass of the bob. If the amplitude is limited to small swings, the period T of a simple pendulum, the time taken for a complete cycle, is:
Objectives
• Determine the period of a pendulum.
•Determine what factors affect the
period of a pendulum.
•Calculate /g/ by using a pendulum.
Materials
1.Pendulum support
2.Meter Stick
3.Metric Mass Set
4.Stopwatch
5.String
6.Masking Tape
7.Clamps
Procedure
1.First, we assembled the support for the pendulum.
2. Then, we suspended the mass from a string and tied it.
3. After, we placed a piece of masking tape below the
suspended mass and lowered the mass, without
swinging, to the tape on the floor. We marked a line
on the tape under the center of the mass used as a
reference point to measure the amplitude of the swing.
4. At last, we established the length of the pendulum
arm by measuring from the center of the mass to a
point on the string and marked the string at the
required length.
Varying Mass
Changing mass
1.For trial 1, 100 g mass.
2.We estimated the location of the center of mass of the pendulum mass and marked it.
3.We suspended the mass from the string in such a way that the length of the entire pendulum from the pendulum pivot point to the center of the mass was 100. Cm.
4.We measured 4.0cm from the reference mark on the floor and marked with a pen the distance.
5.We held a meter stick vertically at the 4cm mark. Pulled the mass to the side so that its center of mass was aligned with the meter stick.
6.We released the mass and started the stopwatch at the same instant. Allowed the pendulum to swing freely whiled we determined the amount of time that it takes to complete 10 cycles.
7.We recorded the data for amplitude, mass, length, and the time in Table 1.
8. We performed the same procedure for the remaining trials but we only kept the same amplitude and length; the mass was increased by 50.g.
Varying Amplitude
Changing Amplitude
1.For Trials varying the amplitude, we repeated the
procedure, keeping the pendulum length the same
and using a 200. g mass. We doubled the amplitude
for each trail (4 cm, 8 cm, 16 cm, and 32 cm). We
marked the amplitudes on the masking tape placed
on the floor as needed to help us find the right
position.
2.We recorded our data in Table 1(trials 6,7,8,9).
Varying Length
Changing Length
1. Applying the same procedure, we used 200 g. mass
and an amplitude of 4 cm, and decreased the
pendulum arm length for each trial by 20 cm (100
cm, 80 cm, 60 cm, 40 cm, and 20 cm).
2.We recorded the data in Table 1(trials 10, 11, 12, 13,
14)
Post Lab Exercises Graphs
Are Proportional
Post Lab Analysis
1.Examine your Data and Graph 1. Does increasing the mass have a significant effect on the period if the length and amplitude remain constant? If so, what seems to be the effect as mass increases? If any effect is noted, is it predicted by the period formula?
A= Ideally it should remain the same period; mass doesn´t affect the period, but because of human error and external forces our calculated periods vary, not too much but they do.
2.Examine your Data and Graph 2. Do small changes in the amplitude of the pendulum have a significant effect on the period if mass and length remain constant? If so, what seems to be the effect as amplitude is increased? If any effect is noted, is it predicted by the period formula?
A= Idealy it should remain the same period becuase amplitude doesn´t affect the period also. But as you know human erro and external forces are dominant.
3.Examine your Data and Graph 3. Does increasing the length of the pendulum have a significant effect on the period if mass and amplitude remain constant? If so, what is the ratio of the periods of the longer pendulums to the periods of the shorter, and are these ratios predicted by the period formula?
A= Yes, increasing the length of the arm increases the period of the pendulum and inversively; decreasing the length of the arm decreases the period of the pendulum.
4.What kind of function is the formula for the restoring force in SHM?
A= as a Linear function
5.Write the formula relating the restoring force to the angle of the pendulum from the vertical position. Assume that the amplitude of the pendulum is small so that Fr is essentially horizontal.
A= Fr= k(sin )θ
6.For small amplitudes of motion (small pendulum angles) can you correctly assume that the restoring force is directly proportional to displacement? Explain your answer from a trigonometric perspective.
A= Yes, it is directly proportional, becuase it has a small; the displacement will be a straight line proportional to the restoring force vector.
7.How does the distance that the center of mass of a pendulum actually travels compare to the amplitude of the pendulum?
A= When the mass is lift higher, the amplitude is increased; since the distance will be longer; therefore as the distance increases the velocity increases.
Conclusions
1. If we are to determine the pendulum´s period, we have to
use short angles because it will affect the period since it will spin
and jabber on. We did observe this in the 32.0 cm amplitude; we
had to make minimum 3 times because of it.
2. Not with an exact data but, we proved that the only parameter that affects the period of a pendulum to change is the length of the pendulum arm.
3.Human error and external forces are
our hindrance to have a more accurate
answer. But I must admit that human error
has been diminished by practice because
I remember the first lab we used stopwatches
our percent erros were above 125% and now the highest one we had was of 7.23%. It is always high but is a huge difference compare to the first one.
Historia de Honduras
Pendulum
12
1
11
10
2
Period
of a
3
9
4
8
7
5
6
La organización político-organizativa TAWAHKA se conoce como la FEDERACIÓN INDÍGENA TAWAHKA DE HONDURAS (FITH), constituida legalmente en el mes de Septiembre de 1987. Ha promovido diversos proyectos a nivel educativo, económico y social en la búsqueda del desarrollo integral del pueblo Tawahka.
- Desde el punto de vista social, los Tawahkas están organizados a partir de la familia extensa. Las mujeres participan en las tareas productivas y juegan un papel central en la reproducción de la cultura. Sin embargo, al igual que otras culturas, su situación con relación al hombre es de desventaja y su aporte en el trabajo doméstico es poco reconocido.