conclusion in simple pendulum experiment

206Conclusion Sample-2004    206ConSam

Sample conclusion for a pendulum experiment lab .   This is probably more than anyone in class will submit (even the “A” reports) but it illustrates as an ideal for which one can strive. Notice that it is typed and spell checked, and should not contain errors such as interchanging “affect “ and “effect”.   Typos may be corrected in pen or pencil if they are not too numerous.

In this experiment we investigated the dependence of the period pf a pendulum on two variable, the mass of the bob and the length of the string. We followed the instructions and tried to keep the amplitude constant for all the measurements so that it would not affect the result, because we learned in class that in the case of a pendulum, large amplitude can change the period. We found that changing the mass from 25 grams to 200 grams did not seem to have much effect on the period, so we concluded that the period is independent of the mass.  

In the case of changing the length of the string, we used strings from 0.25m to 1.5 m long, between the point of suspension and the center of the bob. There was an uncertainty in the measured length because we had to estimate the center of the bob, and the point of suspension. We believe this error to have been less than 10mm(or 0.01m), so for the 1.5m string the uncertainty was only 0.01/ 1.5= 0.6%, while for the shortest string it was .01/. 25=4%. We assumed that the mass of the string was negligible compared to that of the bob. We measured the period using the clock on the wall for 20 swings. It was difficult to read the time to better than 1 second. So if 20 swings took 8 seconds, an error of one second would be 1/8 or 12%, which would be the largest contributor to the error. If we had used 100 swings for each trial the error would be less but we did not have sufficient time.

When we charted and made a trend line with Excel, the period was proportional to the length raised to the0.45 power. This is to be compared with the value in the text that states that the period is proportional to the square root of the length (0.5 power). This is an error of about 10%, which seems reasonable compared to the timing error.

The experiment could be improved by using wire which doesn’t stretch instead of string, greater number of swings and perhaps a watch readable to better than one second.

(Note to students: errors in results are very seldom below 3% and often 10 or 20% depending upon the apparatus, difficulty of the experiment, and time available.)

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Sample lab procedure and report The Simple Pendulum

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27.8: Sample lab report (Measuring g using a pendulum)

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In this experiment, we measured \(g\) by measuring the period of a pendulum of a known length. We measured \(g = 7.65\pm 0.378\text{m/s}^{2}\) . This correspond to a relative difference of \(22\)% with the accepted value ( \(9.8\text{m/s}^{2}\) ), and our result is not consistent with the accepted value.

A pendulum exhibits simple harmonic motion (SHM), which allowed us to measure the gravitational constant by measuring the period of the pendulum. The period, \(T\) , of a pendulum of length \(L\) undergoing simple harmonic motion is given by:

\[\begin{aligned} T=2\pi \sqrt {\frac{L}{g}}\end{aligned}\]

Thus, by measuring the period of a pendulum as well as its length, we can determine the value of \(g\) :

\[\begin{aligned} g=\frac{4\pi^{2}L}{T^{2}}\end{aligned}\]

We assumed that the frequency and period of the pendulum depend on the length of the pendulum string, rather than the angle from which it was dropped.

Predictions

We built the pendulum with a length \(L=1.0000\pm 0.0005\text{m}\) that was measured with a ruler with \(1\text{mm}\) graduations (thus a negligible uncertainty in \(L\) ). We plan to measure the period of one oscillation by measuring the time to it takes the pendulum to go through 20 oscillations and dividing that by 20. The period for one oscillation, based on our value of \(L\) and the accepted value for \(g\) , is expected to be \(T=2.0\text{s}\) . We expect that we can measure the time for \(20\) oscillations with an uncertainty of \(0.5\text{s}\) . We thus expect to measure one oscillation with an uncertainty of \(0.025\text{s}\) (about \(1\)% relative uncertainty on the period). We thus expect that we should be able to measure \(g\) with a relative uncertainty of the order of \(1\)%

The experiment was conducted in a laboratory indoors.

1. Construction of the pendulum

We constructed the pendulum by attaching a inextensible string to a stand on one end and to a mass on the other end. The mass, string and stand were attached together with knots. We adjusted the knots so that the length of the pendulum was \(1.0000\pm0.0005\text{m}\) . The uncertainty is given by half of the smallest division of the ruler that we used.

2. Measurement of the period

The pendulum was released from \(90\) and its period was measured by filming the pendulum with a cell-phone camera and using the phone’s built-in time. In order to minimize the uncertainty in the period, we measured the time for the pendulum to make \(20\) oscillations, and divided that time by \(20\). We repeated this measurement five times. We transcribed the measurements from the cell-phone into a Jupyter Notebook.

Data and Analysis

Using a \(100\text{g}\) mass and \(1.0\text{m}\) ruler stick, the period of \(20\) oscillations was measured over \(5\) trials. The corresponding value of \(g\) for each of these trials was calculated. The following data for each trial and corresponding value of \(g\) are shown in the table below.

Table A3.8.1

Our final measured value of \(g\) is \((7.65\pm 0.378)\text{m/s}^{2}\) . This was calculated using the mean of the values of g from the last column and the corresponding standard deviation. The relative uncertainty on our measured value of \(g\) is \(4.9\)% and the relative difference with the accepted value of \(9.8\text{m/s}^{2}\) is \(22\)%, well above our relative uncertainty.

Discussion and Conclusion

In this experiment, we measured \(g=(7.65\pm 0.378)\text{m/s}^{2}\) . This has a relative difference of \(22\)% with the accepted value and our measured value is not consistent with the accepted value. All of our measured values were systematically lower than expected, as our measured periods were all systematically higher than the § \(2.0\text{s}\) that we expected from our prediction. We also found that our measurement of \(g\) had a much larger uncertainty (as determined from the spread in values that we obtained), compared to the \(1\)% relative uncertainty that we predicted.

We suspect that by using \(20\) oscillations, the pendulum slowed down due to friction, and this resulted in a deviation from simple harmonic motion. This is consistent with the fact that our measured periods are systematically higher. We also worry that we were not able to accurately measure the angle from which the pendulum was released, as we did not use a protractor.

If this experiment could be redone, measuring \(10\) oscillations of the pendulum, rather than \(20\) oscillations, could provide a more precise value of \(g\) . Additionally, a protractor could be taped to the top of the pendulum stand, with the ruler taped to the protractor. This way, the pendulum could be dropped from a near-perfect \(90^{\circ}\) rather than a rough estimate.

What is the pendulum experiment?

Table of Contents

What is the conclusion of simple pendulum experiment?

The surprising conclusion – the pendulum traverses a longer distance in a shorter time, than in a shorter distance, and its period is shorter. There are a number of reasons why Galileo thought that the period remains constant.

How does a pendulum work physics?

The motion of a pendulum is a classic example of mechanical energy conservation. A pendulum consists of a mass (known as a bob) attached by a string to a pivot point. As the pendulum moves it sweeps out a circular arc, moving back and forth in a periodic fashion.

What Newton’s law is a pendulum?

As the pendulum goes back and forth, it is speeding up and slowing down. Newton’s Second Law of Motion tells us that changes in momentum (speeding up and slowing down) generate force, which we can see as the pendulum pulls on the string.

Why is the pendulum experiment important?

Measuring the Effects of Gravity Using math, and the fact that the pendulum oscillates at a constant rate, Galileo was able to determine the approximate effects of the pull of gravity. These early experiments and the use of pendulums allow scientists to calculate the shape of the Earth.

What are the objectives of simple pendulum experiment?

OBJECTIVES : To investigate the functional dependence of the period of a pendulum (τ) on the length of a pendulum (L), the mass of the bob (m) and the starting angle (θo).

What is the introduction of simple pendulum?

Introduction. A simple pendulum consists of a small bob of mass (m) suspended by a light (assumed to be massless) string of length (L), and the string is firmly attached at its upper end. This pendulum is a mechanical system which we will assume exhibits simple harmonic motion .

What affects the period of a pendulum?

The mass and angle are the only factors that affect the period of a pendulum.

Why does length affect the period of a pendulum?

A pendulum with a longer length takes longer to cover the distance to swing from one side to the other. Since the period of a pendulum is the amount of time it takes for the weight to swing and then return to its original position, this will mean a longer period.

Why does a pendulum change direction?

It’s the Earth which is rotating underneath the pendulum, which makes it appear that the pendulum is in fact changing direction. At the North Pole, the pendulum would appear to rotate through a whole 360 degrees once a day, because the Earth rotates all the way round underneath it.

What is a simple pendulum in physics?

A simple pendulum consists of a mass m hanging from a string of length L and fixed at a pivot point P. When displaced to an initial angle and released, the pendulum will swing back and forth with periodic motion.

What causes a pendulum to slow down and stop swinging?

The pendulum stops eventually because of air resistance. The pendulum loses energy because of friction. Only in a theoretical situation when there is no friction the pendulum will oscillate forever.

What forces are acting on a pendulum?

The forces acting on the bob of a pendulum are its weight and the tension of the string. It is useful to analyze the pendulum in the radial/tangential coordinate system. The tension lies completely in the radial direction and the weight must be broken into components.

What are the four laws of simple pendulum?

• 1st law or the law of isochronism: The time period of the simple pendulum is independent of the amplitude, provided the amplitude is sufficiently small.
• 2nd law or the law of length:
• 3rd law or the law of acceleration:
• 4th law or the law of mass:

How does force affect a pendulum?

Either way the principle of periodic motion affects the pendulum. The force of gravity pulls the weight, or bob, down as it swings. The pendulum acts like a falling body, moving toward the center of motion at a steady rate and then returning.

What are 3 examples of pendulums?

Examples of simple pendulums are found in clocks, swing sets, and even the natural mechanics of swinging legs. Tetherballs are examples of spherical pendulums. Schuler pendulums are used in some inertial guidance systems, while certain compound pendulums have applications in measuring the acceleration of gravity.

Why does a shorter pendulum swing faster?

A pendulum with a longer string has a lower frequency, meaning it swings back and forth less times in a given amount of time than a pendulum with a shorter string length.

Who discovered simple pendulum?

June 16, 1657: Christiaan Huygens Patents the First Pendulum Clock.

What is the result of simple pendulum?

T=2π√mk=2π√mmg/L. for the period of a simple pendulum. This result is interesting because of its simplicity. The only things that affect the period of a simple pendulum are its length and the acceleration due to gravity.

What is meant by period of a simple pendulum?

The time period of a simple pendulum: It is defined as the time taken by the pendulum to finish one full oscillation and is denoted by “T”. The amplitude of simple pendulum: It is defined as the distance travelled by the pendulum from the equilibrium position to one side.

What are the procedures for simple pendulum experiment?

Mark a point A on the table (use a chalk) just below the position of bob at rest and draw a straight line BC of 10 cm having a point A at its centre. Over this line bob will oscillate. Find the least count and the zero error of the stop clock/watch. Bring its hands at zero position.

Why simple pendulum is called simple?

The simple pendulum (see wikipedia or hyperphysics) leads to a simple differential equation by using Newton’s second law: ¨θ+glsin(θ)=0. This pendulum gives the easiest way te look at harmonic motion . The above case is what they call the simple pendulum.

How many types of pendulum are there?

The various kinds of pendulums include the bifilar pendulum, the Foucault pendulum, and the torsion pendulum .

What is the equation of motion of simple pendulum?

By applying Newton’s secont law for rotational systems, the equation of motion for the pendulum may be obtained τ=Iα⇒−mgsinθL=mL2d2θdt2 τ = I α ⇒ − m g sin ⁡ θ L = m L 2 d 2 θ d t 2 and rearranged as d2θdt2+gLsinθ=0 d 2 θ d t 2 + g L sin ⁡ If the amplitude of angular displacement is small enough, so the small angle …

What causes a pendulum to slow down?

When the swing is raised and released, it will move freely back and forth due to the force of gravity on it. The swing continues moving back and forth without any extra outside help until friction (between the air and the swing and between the chains and the attachment points) slows it down and eventually stops it.

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Lab Report - Simple Pendulum

Physics for life sciences i (3650:261), university of akron, recommended for you.

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Simple Pendulum July 10, 2018 Avery Apanius & Jordan Crain Babu Gaire Jhena Smith

Abstract: A simple pendulum oscillation pattern is dependent on three variables that act on its motion. Its mass, length, and amplitude are capable of changing the pendulums pattern. In this experiment these variables are tested to obtain an understanding of their role in this system. Each variable will alter the pendulum pattern in a unique way such as elongating or compressing the oscillation period. Introduction: The goal of this experiment was to apply physics principles to a simple pendulum scenario that altered length, mass, and initial angle of motion (amplitude). Data from these tests will be analyzed in order to gain an understanding of the manipulated variables. The data will be in the form of graphs that can show the relationship between the alterations. The graphical component of these tests depends on the period of oscillations measured by a rotary motion sensor. The sensor will record into a program called PASCO ScienceWorkshop 750 interface. Theory: The main equation used through this experiment is T = 2 Sqrt (l / g), which is a simple harmonic oscillator calculation. As you can see, the components of mass, length, and angular motion can be manipulated through this equation. In order to limit error, the rod that is used must be of light weight in order for it to be negligible except when mass is added. A protractor can be used to place the pendulum at the proper angle to increase accuracy of the test. In theory, each manipulation of a variable should yield a new result. It is this information that can be analyzed for patterns. Procedure: For a proper experiment, begin by assembling an apparatus with a rotary sensor attached to a

and L for the length of the string of the pendulum. Based off of this information, it goes to show that of all three factors (, M, L) only the length of the rope has an effect on the period of oscillation. For example, for tests 7, 8 and 9 where we varied the lengths of rope the period of oscillation was 1 sec, 1 sec and 0 sec, respectively. Conclusions: This experiment was intended to investigate and discover what aspects or factors influence or effect the period of oscillation of a simple pendulum. We were able to alter and adjust various factors such as mass, length of the rope, and the initial angle that the pendulum is dropped at. After testing the period of oscillation while varying each factor, we discovered that the period of a simple pendulum is dependent on the length of the pendulum. It is the factor that can increase or decrease the period of a pendulum. Ultimately, all other factors, mass and angle, have no effect on the period whatsoever. This is also clear to tell because length is the only factor other than gravitational acceleration that are included in the equation used to calculate the period of oscillation.

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Course : Physics for Life Sciences I (3650:261)

University : university of akron.

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