Roth+Lab+18

Lab 18 Spring with Mass There is a strong positive, linear correlation between mass and period. The linear fit equation is y=.46x + .406 where x is the mass and y is the period. This is indicated by the r^2 value of .9958. As mass increases, the period increases. The actual equation for period for an oscillating spring is period = 2pi x square root(mass/k). Therefore, as the square root of the mass increases, then the period must also increase.
 * Procedure:**
 * 1) Gather a spring of spring constant 15 N, a hanging mass set, and a stopwatch.
 * 2) Hang the spring off of a ring stand and attach a mass of .5 kg to the spring. Pull the spring down to an amplitude of .06 m from the equilibrium point and record the amount of time it takes to complete 10 oscillations. Divide that time by 10 to determine a single period.
 * 3) Repeat step 3 for masses of .7kg, .9kg, 1.1 kg, and 1.3 kg. Keep everything else constant.
 * 4) Repeat step 3 with everything remaining constant, except change the amplitudes to .03 m, .09m, 1.2m and 1.5m.
 * Data:**
 * Mass vs. Period:**
 * Mass (kg) || Amplitude (m) || Period (s) ||
 * .5 || .06 || .63 ||
 * .7 || .06 || .74 ||
 * .9 || .06 || .82 ||
 * 1,1 || .06 || .90 ||
 * 1.3 || .06 || 1.01 ||

There is a weak, positive correlation between amplitude and period. However, the r^2 value is only .4599, so it is a stretch to even call it a correlation. The linear fit of y= .0052x+.703 is not a good fit. This is because the actual equation for the period of an oscillating spring, period = 2pi x square root(mass/k) is independent of amplitude. Therefore, the amplitude does not affect the period. There is no relationship between amplitude and period.
 * Amplitude vs. Period:**
 * Mass(kg) || Amplitude (m) || Period (s) ||
 * .7 || .03 || .70 ||
 * .7 || .06 || .70 ||
 * .7 || .09 || .71 ||
 * .7 || 1.2 || .71 ||
 * .7 || 1.5 || .71 ||