How the Length of a String Affects the Period and Gravitational Acceleration of a Pendulum: Background | Materials | Procedure | Data | Graphs | Conclusion | Bibliography | Return to Research

Marissa Martin

Background

From, keeping time, to religious practice and recreation, the pendulum has been being used for decades; however, many people are unaware of the complexities that come with the pendulum as well as the physics behind it. For example, when one sees a grandfather clock, they rarely focus on the pendulum inside and how it’s able to swing from side to side repeatedly in exactly one second. When examined, it becomes clear that this process is quite complex, as well as the pendulum itself. To create a pendulum, there is a string or a massless rod that hangs down vertically from an object/surface, or the “point of suspension,” and on the bottom of the string is a bob or a weight that acts as the main mass of a pendulum. Once put together, the pendulum is created and looks similar to Figure A.                                         Figure A Though it is simple in construction, the pendulum has many variables that can be altered in order to receive different results, such as the length of the pendulum string and the angle it is released in order to have it tick every second exactly. With this concept in mind, I came up with a research question involving pendulums; how does the length of the string affect the period and gravitational acceleration of a pendulum? To test this, independent, dependent, and controls will all be used. As explained about, the length of the string will be the independent of the experiment, and the period and gravitational acceleration of the pendulum will be the dependent variables. For the controls of the experiment, the mass of the bob will stay at 1 KG, and the pendulum will always be dropped at a 70 degree angle.

Materials

In order to investigate how the length of a pendulum affects the period and gravitational acceleration of a pendulum, one will need the materials listed below:

• Paper
• Calculator
• A timer
• A pencil
• A computer with internet access
• An online pendulum simulation (the simulation must have a way to alter the length of the string as well as chose the angle at which the pendulum falls)    Simulation

Procedure Top

Before you start, make sure you have a computer, a pencil, paper, and a timer at hand. The first step to the experiment is logging on to the computer at hand, going on any search engine, and looking up “pendulum simulation.” Browse through various simulations until you find one that allows you to change the length of the string and see the angle at which you place your pendulum.  Once this is done, take a piece of paper and make a data table with your pencil, with two columns (label one length in meters and the other time in seconds), and 10 rows (start at trial 1, and count up to trial 10). Once the data table is made, use the simulation to make your string length 0.10 m, write the length in your data table, make sure the mass is 1.00 kg, and place the pendulum at a 70 degree angle. When you release the pendulum, press start on your timer. Keep the timer as you watch the pendulum sway back and forth 12 times (starting at left, to right, and back to left is one (one oscillation)). Once you reach 12, stop the timer, and write the seconds in the time column for trial 1. For trials 2-10, repeat the same process as trial one, but increase the string length by 0.10 m each trial. Continue to place the pendulum at 70 degrees, counting 12 oscillations, timing how long it takes, and recording the data in the corresponding spots.

Data After using the online pendulum simulation, here is the raw data I collected for how the time of the pendulum through 12 oscillations is affected by the length of string.

T=t/12 is then used to calculate the amount of time it took for the pendulum to complete one full oscillation, or the period Next,  g=4pi^2L/T^2 is utilized to calculate the gravitational acceleration for each trial, where L is length and T is period based on the trial Once each gravitational acceleration has been calculated, find the % error by using ( |9.81-g|/9.81)*100 for each g value (9.81 m/s/s is used as the accepted value for gravity). Graphs Top   Data File: Text .:. Excel

Conclusion  Top

For this research assessment, I decided to investigate  the question of how the length of a string affects the period and gravitational acceleration of a pendulum. Once doing my experiment, copying the data, and calculating the various, I have come to a conclusion. When you increase the length of the string on the pendulum, the period also increases; however, the gravitational acceleration isn’t affected by the length of the string, but is more so stays fairly constant the whole time. As shown in the data tables and also in the first graph above, the period of the pendulum increases steadily as the length is also being increased. Since the data was gathered from an online simulation, it seems reliable as there are minimal ways one can accidentally alter the data in a negative way. However, the small increase of the string length (being from 0.10 m to 1.00 m) may have limited the data as it could begin to change later. Additionally, the timing of how long 12 oscillations took may have been slightly off which would weaken the data and alter it overall.

As for the gravitational acceleration, it appears to remain somewhat constant the entire time, meaning that the gravity on the pendulum has little to no change when the string length is increased and/or decreased. But, with the knowledge that accepted gravity is 9.81 m/s/s, and all of these gravitational accelerations are within 7.2 m/s/s and 7.4 m/s/s, the question of errors in the experiment rise. If the timing of the oscillations were originally off, then the data for the gravitational acceleration will also be somewhat incorrect. Additionally, there could have been miscalculations when using the equations to determine the acceleration.

Overall, throughout this investigation, I had to work through various problems and learn how to do a thorough investigation/lab by myself, ultimately resulting in interesting data. When you increase the length of the string on a pendulum, the gravitational acceleration stays almost the exact same, while the period steadily increases as it has farther to travel with the same starting angle. Furthermore, if your grandfather clock was counting seconds faster than it should be, you can increase the string length in order to increase the time it takes to complete a period.

Bibliography

PhysicsLAB: Ripple Tank Sample Solutions,

This is a webpage that explains the motion of the pendulum as well as offers an online simulation

OpenStaxCollege. Introduction to Sociology – 1st Canadian Edition, BCcampus, 23 Jan. 2012,

This link discusses the angular acceleration of a pendulum in regards to gravity

“Pendulum Motion.” The Physics Classroom,

https://www.physicsclassroom.com/class/waves/Lesson-0/Pendulum-Motion

This link is very helpful for understanding a pendulum, it’s motion, and the factors that effect it.

“Pendulum Motion.” The Physics Classroom,

The awesome, interesting science behind a pendulum