Sample Calculations

For a lot of our calculations we used excel to produce graphs and lines of best fit to represent the data that we had collected. For example for the y-acceleration we found the linear line of best fit and compared our slope to the value of the accleration due to gravity. Addtionally other mass we calculated we found the kinetic and potential energy we used the equations K= 1/2mv^2 and U=mgh. We took half of Cam's mass, after converting it from pounds, and multiplied by the velocity vector squared to find the kinetic energy of the motion. And then we took Cam's mass and multiplied it by the acceleration due to gravity and Cam's y-position to find the potential energy of the system. Then to find the total energy we found the sum of these two values, and to get one value for the total energy we averaged all of our total mechanical energies. For the simple harmonic motion of the pendulum we had to calculate the amplitude, period, angular frequecy, and frequency of the motion. We found amplitude by using our y position vs. time graph to find the distance from the line of equilibrium. To find the period we used our x position vs. time graph to figure out the time at which Cam's body leaves the swing. This value is equal to half of the period which made it easy to find. For the angular frequency we plugged our data into the equation ω = √(g/l). And we found frequency by taking the inverse of period (1/T).