By: Thayne Bates, Allie Stricklan, and Brandon England

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.

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.

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

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

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.

Video

Math Model

Energy Balance Spring Left Turning Point Point of Equilibrium Right Turning Point Spring J0 J 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 J J0 J Total Energy Data found using the equation kE=1/2 mv² Left Turning PointPoint of EquilibriumRight Turning Point J

E=1/2(k1 + k2) A²

Data Spring∆yk=(ma)/∆y Spring m42.65 Spring m39.24 Massf=1/Tω kg Hz kg Hz kg Hz Massf=1/Tω kg kg kg Calculated Measured

Conclusions  After measuring the displacement, we found the k constants to be roughly and  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.

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.