# Simple Harmonic Motion

04/04/2012

Simple Harmonic Motion Lab

Introduction:

In this two part lab we sought out to demonstrate simple harmonic motion by observing the behavior of a spring. For the first part we needed to observe the motion or oscillation of a spring in order to find k, the spring constant; which is commonly described as how stiff the spring is. Using the equation Fs=-kx or, Fs=mg=kx; where Fs is the force of the spring, mg represents mass times gravity, and kx is the spring constant times the distance, we can mathematically isolate for the spring constant k. We can also graph the data collected and the slope of the line will reflect the spring constant. In the second part of the lab we used the equation T=2πmk, where T is the period of the spring. After calculating and graphing the data the x-intercept represented k, the spring constant. The spring constant is technically the measure of elasticity of the spring.

Data:

mass of weight | displacement|

m (kg)| x (m)|

0.1| 0.12|

0.2| 0.24|

0.3 | 0.36|

0.4| 0.48|

0.5| 0.60|

We began the experiment by placing a helical spring on a clamp, creating a “spring system”. We then measured the distance from the bottom of the suspended spring to the floor. Next we placed a 100g weight on the bottom of the spring and then measured the displacement of the spring due to the weight . We repeated the procedure with 200g, 300g, 400g, and 500g weights. We then placed the recorded data for each trial into the equation Fs=mg=kx. For example: 300g weight mg=kx

0.30kg9.8ms2=k0.36m 0.30kg 9.8ms20.36m=k

8.17kgs=k

Here we graphed our collected data. The slope of the line verified that the spring constant is approximately 8.17kgs.

In the second part of the experiment we suspended a 100g weight from the bottom of the spring and pulled it very slightly in order to set...

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