2. HOOKE’S LAW The Period of an Oscillating Spring

3. Purpose Graphically determine the spring constant, K, of a spring using a Hooke’s Law Apparatus Determine the relationship between mass and period of an oscillating spring using graphical methods Determine the spring constant, K, from the period and mass of an oscillating spring.

4. Hooke’s Law In a mass-spring system, the force acting to extend the spring is directly proportional to, but opposite in sign to, the displacement of the mass extending the spring. F = -Kx K is the spring constant (Units N/m)

5. Hooke’s Law Apparatus

6. Hooke’s Law Apparatus with weights

7. Procedure – Part I Use Hooke’s Law Apparatus to determine spring constant, K. Start with apparatus at zero extention. Place one mass on spring holder. Record mass (m) and extension (x) in meters.

8. Procedure Continued… Repeat previous two steps for four more masses. For each additional mass record cumulative mass and cumulative extension. Graph Force (F) v. extension. Remember to convert mass into force since this is a vertical situation.

9. From this graph of force versus extension determine the spring constant using the appropriate regression. Print graph.

10. Procedure – Part II Determine the relationship between period and mass for an oscillating spring.

11. Procedure Set up spring-holder on pendulum apparatus so that spring can oscillate freely. Set height at about 0.50m and place Motion Detector face-up under the spring holder. Set Motion Detector program at 50 readings/s for 5 seconds.

12. Procedure Continued… Place mass on holder and set into motion. Start Motion Detector. After program runs check distance v. time graph and position v. time3 graph. By inspection determine the frequency of the oscillation of the spring.

13. Print graph. Repeat procedure for four additional masses. For all five trials, graph T vs. m and T2 T2 vs. m. Do appropriate regressions on each graph to find proper direct relationship between T and m.

14. …and more… Determine the value of K from the final two graph generated from this experiment.

15. How many graphs? You should have seven total graphs. Five (5) sinusoidal regressions for the five oscillations with the frequency indicated on each one. A plot of T vs. m with a regression. A plot of T 2 vs. m with a regression.