Pendulum Lab Write-up Going into the lab, we were told that the two things that effect the way a pendulum works was the length of the pendulum. Weight and angle of elevation didn't effect the way the pendulum acted. From this information, my teammates and I came up with a table to compare how the length of the pendulum (in meters) was related to the period of the swings. (Period= seconds/swings). After we got a number of values in our table, we proceeded to graph the values in x, y format i.e.: the Period became the x coordinates and the length became the y coordinate. The resulting graph looked parabolic. With this information, we now knew what the basic formula for determining the relationship of Length and Period had to be f (x)= x^2. We plugged in one of the sets from out table and came up with the two sides not equaling each other.
Now since the vertex had to be (0,0), because a pendulum length of 0 would mean there is no pendulum, we didn't have to worry about translations of the graph; however, since the basic formula y=x^2 didn't work, the only possible solution was to multiply the period by some constant. We named this constant M. Since the period represented the x and the length represented the y, we simply substituted in our own variables and came up with the formula Length = (M*Period)^2. To find M, all we had to do was plug in one of our sets of values from our table and solve. M came out to be .48; and so the final formula came out to be Length = (.48 * Period)^2.
1. Make a table of values comparing the Length of the Pendulum and the period.
2. Graph the values using Period to represent x and Length to represent y 3. Deduce the mother function and plug in numbers 4. Find the constant M and substitute in all variables Discussion/Analysis The main source of error is the fact that the string can be stretched so it is confusing weather to make the string as taut or keep it loose. Also, there is a lot of human error that occurs when timing the swings. The time it takes for our eyes and minds to realize the string has started to swing wasn't deducted from the computations.
Ideas for further applications This lab could be used to find the height of a school building, or a poster!