Roth+Lab+17

Lab 17 Simple Pendulum There is a weak, negative correlation between mass and period. The r squared value is only .5052, so the linear model is not a perfect fit. This may be due to the limited number of trials. However, no other mathematical models fit the data any better, so it appears that as mass increases, period decreases. The linear fit equation is Period= -.07(Mass) + 2.115. However, another possibility is that mass and period are not related, which could explain the weak correlation. The equation for the period does not include mass, so this is a likely possibility.
 * Procedure:**
 * 1) Gather the following supplies: 1 meter of string, a hanging mass set, and a stopwatch.
 * 2) Make sure that tie a mass of .5 kg to the 1 meter of string and tie the string to some item that is elevated high enough to give clearance for the 1 meter of string and mass combination.
 * 3) Hold the mass and string at a 37 degree angle from the mass’s equilibrium position and let go. Measure the amount of time it takes to make 10 periods. Divide that number by 10 to determine the period.
 * 4) Repeat step 3 for masses of .7 kg, .9 kg, 1.10kg, and 1.30 kg.
 * 5) Repeat step 3 for angles of 10 degrees, 20 degrees, 30 degrees, and 50 degrees.
 * 6) By untying the string from its hanger and retying it, the string length can be changed. Repeat step 3 for string lengths of .9m, .8m, .7m, and .6m.
 * Mass vs. Period:**
 * Mass (kg) || Period (s) || Angle (degrees) || String Length (m) ||
 * .5 || 2.10 || 37 || 1 ||
 * .7 || 2.03 || 37 || 1 ||
 * .9 || 2,06 || 37 || 1 ||
 * 1.10 || 2,05 || 37 || 1 ||
 * 1.30 || 2.02 || 37 || 1 ||

There is a weak positive correlation between angle and period. The r^2 value is only .7095. This could be explained by the fact that angle and amplitude are independent of period, since the equation for period does not include the angle of amplitude. That equation is period = 2 pi x (square root(length/gravity). Therefore, there is no relationship between angle and period.
 * Amplitude (Angle) and Period:**
 * Mass (kg) || Period (s) || Angle (degrees) || String length (m) ||
 * 1.3 || 2.01 || 10 || 1 ||
 * 1.3 || 2.01 || 20 || 1 ||
 * 1.3 || 2.04 || 30 || 1 ||
 * 1.3 || 2.02 || 37 || 1 ||
 * 1.3 || 2.06 || 50 || 1 ||

There is a strong positive correlation between length and period. The r^2 value is high of .9897. Therefore, the equation of y=1.332x + .7352, with length as x and period as y, is a good linear fit for the relationship. The equation for period, which is period = 2 pi x (square root(length/gravity) shows that the square root of the length affects the magnitude of the period. Therefore, it makes sense that an increase in length would cause an increase in period.
 * Length vs. Period:**
 * Mass (kg) || Period (s) || Angle (degrees) || Length (m) ||
 * 1.3 || 1.94 || 37 || .90 ||
 * 1.3 || 1.835 || 37 || .80 ||
 * 1.3 || 1.65 || 37 || .70 ||
 * 1.3 || 1.529 || 37 || .60 ||
 * 1.3 || 2.05 || 37 || 1 ||