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SC 441 PHYSICS LAB Presentation The Simple Harmonic Motion

SC 441 PHYSICS LAB Presentation The Simple Harmonic Motion. New York City College of Technology Student: Hao Wu Professor: Roman Kezerashvili Dec.20.2002. Objectives:. To study the simple harmonic motion by investigating the period of oscillation of a spring.

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SC 441 PHYSICS LAB Presentation The Simple Harmonic Motion

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  1. SC 441 PHYSICS LABPresentationThe Simple Harmonic Motion New York City College of Technology Student: Hao Wu Professor: Roman Kezerashvili Dec.20.2002

  2. Objectives: • To study the simple harmonic motion by investigating the period of oscillation of a spring. • To determine the force constant Kof the spring for one spring and two spring series.

  3. Equipment: • .Two springs • .Photogate accessories • .Set of masses • .Science Workshop Interface box • .Triple-beam balance

  4. The Newton’s second law: F = ma m is mass (kg) a is acceleration of motion(m/s²) The Hook’s law: F = -kx k is force constant for spring (N/m) x is the displacement of spring (m) Theory:

  5. K = 4 л²(M + ms/3)/T² M is mass of applied force (kg) msis mass of spring(kg) T is the time period (s) K = ( k1 k2 ) / ( k1+k2 ) k is the force constant of the spring system k1 is the force constant of the spring1 k2 is the force constant of the spring2 F = ma = - kx a = - kx / m

  6. Diagram of simple harmonic motion use spring

  7. Procedure: • Hangs the masses m on the spring that is larger than spring mass. • Pull down the spring with masses,and pass through the photogages,then release it smoothly. • After 10 cycles of the oscillation, stop the spring and record mean values of period T and frequency f. • Increase the hanging masses and repeat the above processes, record the data as masses are 0.2, 0.3, 0.35, 0.37 and 0.4 kg. • Use spring 2 and spring series which is two spring connected each other repeat the above processes.

  8. Table 1. Data for Spring 1 Mass of spring is 0.181 kg

  9. Graphic of Spring 1

  10. Computing results for spring 1 Mean value of k from experiment is 8.6(N/m) Liner function y = ax + b a = k / 4 л² K = 4 л² Slope K from the slope of graph is 9.07(N/m) Difference 1.3%

  11. Table 2. Data for Spring 2Mass of spring is 0.035 kg

  12. Table 3. Data of Springs in seriesMass of springs is 0.216 kg

  13. Spring 2 Mean value for k is 34.9 (N/m) K from the slope of graph 28.64 (N/m) Difference 4.9% Spring Series Mean value for k is 6.5 (N/m) K from the slope of graph 7.0 (N/m) K from the k=(k1k2)/(k1+k2) 6.9 (N/m) Difference 0.5% Calculation results for Table 2 and Table 3

  14. Analysis and compare the data from the experiment

  15. Conclusion: This experiment uses simple harmonic motion to investigate and verified the spring motion and find out the K which is the force constant for spring. Use Hook’s law F = -kx can determine the relation with force constant of spring K and its displacement. After analyzed table 1, 2 and 3, I found when the masses was added the period of time T was increased. The frequency getting decreased,and T = 1/f. When used spring system to replace the single spring, the spring series K became a small value. It’s value is less than any individual spring in the system.

  16. The End Thank You

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