A lab I'm assigned concerning simple harmonic motion uses a simple spring attached to a mass system...it asks me to "investigate the period-mass relationship. determine the period of oscillation of your system for several different masses. Verify that your data is consistent with the predicted period mass relationship "T=2pi sqrt of [(m+m(eff))/K] Construct a graph of (period)^2 vs mass. Justify your conclusions. Employ % difference calculations where appropriate.
My data was
mass 50.95g, went down 2.1cm from equilibrium, period=3.22 sec
mass 70.95g, went down 2.8 cm from equil, period=3.8 sec
mass 100.95, went down 4.0 cm from equil, period=4.04 sec
mass 120.95g, went down 4.9cm from equil, period=4.9sec
mass 140.95g, went down 5.7cm from equil, period=5.7sec
The Attempt at a Solution
Using f=-kx, i found the avg spring constant to be 243.54. I need to find the period of oscillation for all of the masses using the equation above and compare that to the period of oscillation I got in the actual experiment. I tested it out... so T=2pi (square root[50.95/242.6])...gives me T^2=1.32 or T=1.14... this is no where near 3.22sec which was my actual experimental result. The lab says that you should be getting within 1% error...is my data just very inaccurate or am I doing something wrong?