1. By: Thayne Bates, Allie Stricklan, and Brandon England

2. Summary  The purpose of this experiment was to find the spring constant of two different springs and determine the elastic energy between the two. We then had to use Newton’s Law to prove that a(t)=(-(k1 + k2)/m) x (t) is true and by using the equation ω²=(k1+k2)/m we get ω=-√((k1+k2)/m). After comparing our measured values with the calculated values, we could confirm that the equations are true.  Measured and Calculated Data can be found in the tables on the Data slide.

3. Introduction  In this experiment, we used 2 different springs and by adding weights, we found the spring constants. We built a device with an air slide to find the elastic energy in the springs.

4. Materials  2 Similar Springs  Air Slider  Weights of Different Masses  Hooks and Rings to Support Springs  A Video Camera

5. Procedure 1. Build a system with a spring hanging from some object and a weight hanger connected to the bottom of the spring. 2. Measure the mass of the weight hanger. 3. Record the position of the weight hanger. 4. Place a weight on the hanger and record the change in position. 5. Calculate the k constant of the spring. 6. Repeat for the second spring

6. Procedure (continued) 1. Build another device using an air slide and an air slide glider with a spring attached to each end. 2. Slightly tap one end of the glider and record the oscillation times for the glider with 3 different masses. 3. Use the given equations to determine ω.

7. Video

8. Math Model

9. Energy Balance Spring Left Turning Point Point of Equilibrium Right Turning Point Spring 11066.25 J0 J1066.25 J Spring 2981 J0 J981 J Data found using the equation E=1/2(k1 + k2) A² Left Turning Point Point of Equilibrium Right Turning Point Glider0 J2047.25 J0 J Total Energy Data found using the equation kE=1/2 mv² Left Turning PointPoint of EquilibriumRight Turning Point 2047.25 J

10. E=1/2(k1 + k2) A²

11. Data Spring∆yk=(ma)/∆y Spring 1.115 m42.65 Spring 2.125 m39.24 Massf=1/Tω 1.110 kg.91715 Hz5.76262 2.210 kg.73674 Hz4.62907 3.310 kg.62630 Hz3.93516 Massf=1/Tω 1.110 kg.886145.56776 2.210 kg.641344.02965 3.310 kg.527863.31662 Calculated Measured

12. Conclusions  After measuring the displacement, we found the k constants to be roughly 39.24 and 42.65.  The equations were proven to be true.  The difference in the recorded ω and the calculated ω can be seen in the table in the Data slide.

13. Acknowledgments We would like to thank Mr. Walfred Raisanen for assigning this wonderful experiment. We would also like to thank ourselves for being smart enough to complete the assignment.