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Pendulum Periods

This physics experiment explores how the period of a pendulum changes with variations in length, amplitude, and mass. By measuring and analyzing the data, the relationship between these factors and the period is uncovered. Using materials like a Vernier Photogate, protractor, and string, the procedure involves conducting tests with different parameters to observe the effects on the period. The results reveal that the period is primarily dependent on the length of the pendulum, showing a proportional relationship between T^2 and L.

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Pendulum Periods

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  1. Pendulum Periods Artur Nisonov (Regents Physics) Mechanical Engineer Alon Kadashev (Regents Physics) Electrical Engineer August 30, 2004

  2. Overview • Objective • Background • Materials • Procedure • Results

  3. Background The velocity will be equal to the circumference of the circle which is the distance traveled divided by the time it took, v=2πA/ T => T= 2πA/ v From conservation of Energy => 1/2m(v^2) + 1/2k(x^2)=1/2k(A^2) Getting the relation=> (A/v)=(m/k)^1/2 Combining all the formulas => T= 2π(m/k)^1/2

  4. Background (cont.) For small angles => F=-mgsin(θ)~ -mgθ Arc length => L=xθ Combining the two equations => F~ -mg(x/L) According to Hooks law => F=-kx where k=mg/L Going back to the previous equation T= 2π(m/k)^1/2 substitute for k and we get T= 2π(L/g)^1/2

  5. Objective • Measure the period of a pendulum as a function of amplitude • Measure the period of a pendulum as a function of length • Measure the period of a pendulum as a function of bob mass

  6. Power Macintosh or Windows PC LabPro or Universal Lab Interface Logger Pro Vernier Photogate Protractor String Two ring stands and pendulum clamp Mass Bob Meter stick Graphical Analysis or graph paper Materials

  7. Procedure • Take a 1 m long string tie it up to the stand on the table. • Attach a Photogate underneath the string, so that when you attach the mass weight it will pass freely through the Photogate. • Part I, amplitude test, change the angle three times, and see how it affects the period. • Part II, length, change the length three times, and monitor how it affects the period. • Part III, attach three different mass weights and observe the period will it change, record the data each time.

  8. Results • Discover that the period is only relation to the length of the string. • Find out that T^2 is proportional to L.

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