Simple Pendulum Experiment Report
A simple pendulum may be described ideally as a point mass suspended by a massless string from some point about which it can swing back and forth in a place. A simple pendulum can be approximated by a small metal sphere with a small radius and a large mass compared to the length and mass of the light string from which it is suspended. If a pendulum is set in motion, swings back and forth, its motion will be periodic. Thus, GISHOMEWORK prepares this article to provide more information on a simple pendulum experiment report.
The time that it takes to make one complete oscillation is defined as the period T. Another useful quantity used to describe periodic motion is oscillation frequency. The frequency f of the oscillations is the number of oscillations that occur per unit time and is the inverse of the period, f = 1/T. Similarly, the period is the inverse of the frequency, T = l/f. Finally, the maximum distance that the mass is displaced from its equilibrium position is defined as the oscillation amplitude.
Simple Pendulum Experiment Theory
When a simple pendulum is displaced from its equilibrium position, a restoring force moves the pendulum back towards its equilibrium position. As the pendulum’s motion carries it past the equilibrium position, the restoring force changes its direction so that it is still directed towards the equilibrium position. If the restoring force F is opposite and directly proportional to the displacement x from the
equilibrium position, so that it satisfies the relationship below:
F= -k x ……. Equation 1
then the motion of the pendulum will be simple harmonic motion, and its period can be calculated using the equation for the period of simple harmonic motion calculated as:
It can be shown that if the amplitude of the motion is kept small, Equation 2 will be satisfied, and the motion of a simple pendulum will be simple harmonic motion, and one can use equation 2.
Diagrammatic illustration of a force that restores a simple pendulum
The restoring force for a simple pendulum is supplied by the vector sum of the gravitational force on the mass. Mg, and the tension in the string, T. The extent of the restoring force depends on the gravitational force and the displacement of the mass from the equilibrium position, in the figure above, where a mass m is suspended by a string of length l and is displaced from its equilibrium position by an angle theta and a distance x along the arc through which the mass moves. The gravitational force can be resolved into two components, one along the radial direction, away from the point of suspension, and one along the arc in the direction that the mass moves.
The component of the gravitational force along the arc provides the restoring force F, which is determined as follows:
F = – mg sinθ …… equation 3
where g is the acceleration of gravity, theta is the angle the pendulum is displaced, and the minus sign indicates that the force is opposite to the displacement. For small amplitudes where theta is small, sin theta can be approximated by theta measured in radians. Therefore
F = – mg θ …… equation 4
The angle theta in radius is x/l, is the length of the arc divided by the length of the pendulum or the radius of the circle in which there is the mass movement.
And as a result, the force of restoration is given as follows:
F = – mg(x/l) …… equation 5
The restoring forced is directly proportional to x, the displacement, and is represented by equation 1 where k=mg/l. when one substitutes the value of k in equation 2, therefore, the period of a simple pendulum is determined as follows:
….. equation 6
….. equation 7
Thus, for small amplitudes, the period of a simple pendulum depends only on its length and the value of the acceleration due to gravity.
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What are the Sources of Error in Simple Pendulum Experiment?
Generally, the pendulum length usually presents errors given that people determine and measure to the bottom and not the centre of mass. Secondly, there is uncertainty at the top position; for instance, a loop with a knot clamps the string in use between two metal blocks. This is to ensure that there is a clear point where the pendulum starts to swing.
If you are asking yourself, what factors affect the period of a pendulum? The following are some of the key factors, errors due to time: error in counting where one is likely to make incorrect counts. For example, when one releases the pendulum, they say one instead of zero. Also, the timing interval is not long enough. In addition, other common problems that lead to errors are the instruments themselves. Lastly, having a stopwatch that times 0.001 seconds does not mean that the uncertainty is of the same order. The uncertainty will certainly almost be from the person operating the stopwatch button.
What Is the Aim of Simple Pendulum Experiment?
The key aims of a simple pendulum experiment are: to examine and study the motion of a simple pendulum; secondly, to study simple harmonic motion, third is to learn the definitions of the period, frequency, and amplitude; fourth, to learn the relationships between the period, frequency, amplitude and length of a simple pendulum and lastly, to determine the acceleration due to gravity using simple pendulum lab report graph.
Simple Pendulum Lab Report Procedure
While following the simple pendulum lab report procedure, it is vital to determine the acceleration due to gravity. Although there are several, and you can always find an available lab report template, it is advisable to generate your report as long as you use the suitable lab report format. Also, ensure that you take note of all the simple pendulum experiment calculations.
- The simple pendulum is composed of a small spherical ball suspended by a long, light string attached to a support stand by a string clamp. The string should be approximately 120 cm long and clamped by the string clamp between the two flat pieces of metal so that the string always pivots about the same point.
- Use a vernier calliper to measure the diameter d of the spherical ball and from this calculate its radius r. Record the values of the diameter and radius in meters.
- Prepare an Excel spreadsheet to adjust the length of the pendulum to about .10 m. The length of the simple pendulum is the distance from the point of suspension to the centre of the ball. So first, measure the length of the string ls from the point of suspension to the top of the ball using a meter stick. Next, make a table and record this value for the length of the string. Next, add the radius of the ball to the string length and record the value obtained as the length of the pendulum.
- Displace the pendulum about 10º from its equilibrium position and let it swing back and forth. Measure the total time that it takes to make 50 whole oscillations. Record that time in your spreadsheet.
- Increase the pendulum length by about 0.20 m and repeat the measurements made in the previous steps until the length increases to approximately 2.0 m.
- Calculate the period of the oscillations for each length by dividing the total time by the number of oscillations, 50. Then, record the values in the appropriate column of your data table.
- Draw a graph of the period of the pendulum as a function of its length. The pendulum length is the independent variable and should be plotted on the horizontal axis or x-axis. The period is the dependent variable and should be plotted on the vertical axis or ordinate (y-axis).
- Use the trendline feature to draw a smooth curve that best fits your data.
- Examine the power function equation that is associated with the trendline. For example, does the power function suggest the relationship between period and length as illustrated in equation 7?
- Examine your graph and notice that the change in the period per unit length, the slope of the curve, decreases as the length increases. This indicates that the period increases with the length at a rate less than a linear rate. The simple pendulum theory and Equation 7 predict that the period depends on the square root of the length.
- Square the values of the period measured for each length of the pendulum and record your results in the spreadsheet.
- Use the chart feature again to graph the period squared, T2, as a function of the length of the pendulum l. The period squared is the dependent variable and should be plotted on the y axis. The length is the independent variable and should be plotted on the x-axis.
- Examine your graph of T2 versus l and check to see if there is a linear relationship between T2 and l so that the data points lie along a line.
- Use the trendline feature to perform a linear regression to find a straight line that best fits your data points
- Adjust the length of the pendulum to about 0.8 m. Measure the pendulum period when it is displaced 100, 150 200 250 300 350, 400 450, and 500 from its equilibrium position. Make a table to record the period T as a function of the amplitude A.
- Using your data, make a graph of the period versus the amplitude.
- Measure the length of the pendulum and use Equation 7 to calculate the period of the pendulum. Then, add this theoretical point to your graph for the period with zero amplitude.
What Is the Structure of Laboratory Report?
Before you write a lab report, it is essential to understand the 7 parts of a lab report? But, then, you do not have to stress anymore. This is because GISHOMEWORK experts present to you a summary of a suitable lab report format.
What Are the 7 Parts of a Lab Report?
An ideal lab report would include the following parts:
- The title
The title page, abstract, references, and appendices are written on separate pages in the form of subsections from the main body of the report. Double-line spacing is the recommended style in spacing the text, 12 is the required font size, and always remember to include page numbers.
Your report should be cohesive, and all arguments should link the prediction in the introduction to the context in your discussion section.
The title page must indicate what the report is about. Also, it must entail the variable under investigation and should be written in the form of a question.
It would help if you always wrote this last. First, the abstract is the precise and comprehensive summary of the whole report. Second, it should be brief and never in points form. And lastly, it should provide straightforward explanations.
The introduction must provide a rationale for the research study. By so doing, the introduction explains the genesis of your hypothesis. Generally, the introduction should have a funnel structure. You begin by providing a broad overview as you narrow it down to be more and more precise. The objectives should never seem to be out of thin air, and instead, it should be logical into the purposes and the hypothesis.
The methodology plays a key role in your research study. Therefore, you must take your time and establish a realistic and comprehensive method. The method should include the following subheadings:
- Participants – here, include the number of participants recruited during the research. State how the sample was obtained and give vital demographic details relevant to the study, such as gender, age range, standard deviation, etc.
- Research design – state the design of the experiment. Next, indicate the dependent and independent variables. Also, mention how the DV and IV operationalized and identify any possible control used, such as counterbalancing.
- Materials – list all the used materials and their corresponding measures. For instance, mention the title of the questionnaire is used for the study in question.
- Procedure – provide a detailed description of the used procedures when conducting the study. Provide all necessary information that would make it possible for replication and improvement of the same in future.
This is the section of the paper that details the descriptive statistics followed by inferential figures. Report the standard deviation, mean, and confidence intervals (CIs) of 95% for every IV level. Also, name the statistical test being utilized. Ensure that you report appropriate statistics such as p values. Indicate the magnitude, the significance of the results, and the direction of the outcome, such as which category performed better? Use the APA style.
Provide all the findings in simple English and link your findings to your hypothesis. Say whether it is rejected or supported. Next, compare all your results to background materials from the introduction. Are they similar, or is there a difference? Next, indicate the results’ confidence level and suggest constructive ways of improving the study. In the concluding paragraph, finish with a statement of the key points and findings of the discussion, that is, the implications and interpretation in at most 4 sentences.
A reference is a list of all the sources you have cited in the essay—this list is written in alphabetical order.
How Do You Write a Lab Summary?
Using the handout or manual and notes taken while in the lab as a base guide, describe the experimental procedure followed in paragraph form.
Make sure that your data makes sense to you and to any other party who would be interested in reading your report. Use relevant tables, review the data, and summarize the findings in different paragraphs.
Establish a context for the lab. State the scientific concept clearly, prelab question 1, state how the attainment of the key objectives in the lab prelab question 2 and 3 helped in learning the scientific concept, and state your hypothesis.
Clearly and comprehensively discuss and interpret the findings of the lab.
Focus on what you have learned by doing the lab experiment. In a paragraph, summarize all that you have learned regarding the scientific concept and in the second paragraph, provide additional information relevant to the concept from the lab.
Summarize the entire report.
Capture the essence of the report and acknowledge the sources used.
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