Simple Harmonic Motion Lab Question: Investigating the Period-Mass Relationship

[jonesy3]

Homework Statement

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.

Homework Equations

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?

 

[SGT]

Homework Statement

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.

Homework Equations

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?

What do you mean by went down x cm from equilibrium? Did you hang the mass and measured the new equilibrium point relative to the equilibrium of the unloaded spring, or did you measure the amplitude of the oscillation relative to the loaded equilibrium?

 

[Kurdt]

I'd have to say be careful with units. The value for spring constant you have obtained is certainly not Newtons per meter. In your calculation you've used grams instead of kilograms. I'd recommend sticking with SI units. Plus have you measured frequency or time period in your experiment?