Beats by Lilly Lab Report Introduction: Testing: Our Role, Task, and Stakeholders: We as a business group in the field of design seek to make a pendulum swing to any beat in order to create a light that moves to the beat of any song for our client, One Dimension. Constraints and Criteria: Some constraints that we must have include a pendulum that has the ability to swing to a song of any frequency, a ring stand, washers, and string. Some criteria that we would like to have included a visual representation of the steps taken in our lab (such as a PowerPoint), a pendulum that is consistent with more than just the two songs from class, and a simple equation that can be used to figure out the value of the independent variable for a certain dependent variable. During testing, it was important to change numerous variables in order to encounter one that has the largest impact on the speed of the pendulum. Through numerous tests, we noticed that the length of the string for the pendulum had the greatest impact on its speed. First, we altered the number of centimeters back from which we let the pendulum go. Overall, the speed of the pendulum only varied by one-tenth of a second between ten centimeters, demonstrating that this was not a very influential factor; therefore, we moved on to changing the length of the string. At each length, we also pulled the string back to a certain set of distances in order to be able to manipulate the length based on the period of the song. Through our testing, we measured the period of the song: this later referred to the time elapsed between each beat of a specific song. We altered the period based on the number of centimeters back at which we let the pendulum go.
Here is a photo of our group with our pendulum created at school. Here is the pendulum testing at work, as I pull the string back to a certain length using a meter stick. I also created a pendulum at home with the same characteristics in order to complete all the necessary data. Data: Table of Testing Results: There are numerous data tables due to the numerous tests done at varying heights with varying lengths to which the string was pulled back to. centimeter pull-back centimeter pull-back 3 centimeter pull-back.696.96 3.78 4.55 5.45 6 38.98 3.7 4.68 5.43 6 4 3.86 4.33 5.43 6 73
4 centimeter pull-back 5 centimeter pull-back 4.38 5.47 6.6 5 8 6.64 Graph of Testing Results: There are also numerous graphs due to the numerous tests done with varying heights and pull-back lengths. These graphs have different relationships based on the number of points found during testing. If there are fewer points, there is more room for inaccuracy and linear graphs. There is also no graph for the fifty centimeter height, as two points was not sufficient to create an accurate graph. cm Pull-Back of and its Impact on the y =.63x + 83 R² =.987 Linear ( period) 4 6 8 This graph has a root relationship.
cm Pull-Back of and its Impact on the 4 6 8 y =.44x +.6886 R² =.9974 Linear (Time per period) This graph has a linear relationship, but seems a bit exponential as the length of the string pulled back increases. 3 cm Pull-Back of and its Impact on the 4 6 8 y =.9x +.7934 R² =.9979 Linear ( period) This graph has a linear relationship, but seems a bit exponential as the length of the string pulled back increases..7.6.4.3 4 cm Pull-Back of and its Impact on the 4 6 8 This graph has an exponential relationship. y =.5x +.97 R² =.9845 Linear ( period)
Linearized Graph: This is the table and graph for our linearized graph at a ten centimeter pull-back length, which was used during our performance. Since this was a root function, we kept the y values the same, but altered the x values to (x^). When a graph was created with these values, the graph became linear. Linearized 3.67766.696 4.473595.96 5.477558.78 6.345553.55 7.7678.45 7.74596669 38 Linearized cm Pull-Back of and its Impact on the 5 y =.86x +.43 R² =.9949 Linear ( period with linearization) Linearized Equation: Our equation is as follows: T =.86 (h^) +.43 for cm pull-back where T = period where h = string Using the data and the linearized equation that comes from it, our group would be able to change the prototype to move to the beat of any song. The beats per minute will provide us with the period, so using the y axis as a guide, we can move to the right to see the height that corresponds with such period. Another simple way is to plug in a value of T into the equation and solve for h. Performance: Our pendulum successfully swung to the beat of both our self-chosen song and clientchosen song for fifteen seconds during our performance. Through the use of the equation derived from our testing, our pendulum and prototype worked extremely well. The pendulum swung to the song All of Me, with 8 beats per minute, on each beat, but for the challenge song, Bye Bye Bye, with 8 beats per minute, the pendulum swung to every other beat, as to not move too quickly when being converted to a light system. Overall, our group executed the performance portion of the lab well.
Discussion of Future Changes: Overall, our group did a wonderful job and was able to successfully create a pendulum that can swing to the beat of any song for our clients of One Dimension. We also quickly found an equation that could be used to find the height at which our pendulum must stand for the client's mystery song. The data turned out to be accurate and extremely useful. But, even with the successes that took place towards the end, there were numerous challenges throughout the process. For starters, our initial data collecting was not as useful, which resulted in extra testing at home and over the course of numerous days in class. Also, the equation was hard to interpret with the variables at hand: we were unsure at first where each piece of our data would eventually fall. In the end, though, the difficulties proved to be worthwhile for our successful performance. To continue work with this project, it would seem useful to test the pendulum at reasonable heights for the light, such as in meters. That way, the data collected will be based off of a measurement that is logical for the task at hand. Also, the weight of the light must be put into consideration, as it is much larger than the mass of five washers. One thing that could be changed for the next data collection is using a protractor rather than a ruler to consider angles with the pendulum. That way, there can be more accuracy over the usage of a meter stick in the life-size prototype.