Lab 1 Pendulum and Spring

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Jan 9, 2024

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PHY 121 Lab: Pendulum and Spring Chris Nixon Summary: The students investigated two systems that resemble simple harmonic motion in this experiment: a mass on a spring and a simple pendulum. The students should be able to decide which aspects of the systems make them similar to simple harmonic oscillators and which properties prevent them from being actual simple harmonic oscillators through thorough examination. An oscillator, or a system with a periodic back and forth motion, is a very es- sential sort of system. This is due to the fact that many natural systems are oscillators or may be approximated using an oscillator model. A variety of natural systems exhibit harmonic oscillations, or periodic motion with a pre- ferred or natural frequency that depends on other system features. Ulti- mately, the students timed the pendulum swinging through 20 complete cy- cles/periods for five different lengths: 0.2m, 0.4m, 0.6m, 0.8m, and 1.0m. The mass of the pendulum bob was measured using a triple-beam balance, then suspended from a one-meter-long string using mounting rods and clamps to produce a pendulum. The data that was obtained was consistent with the expectations.
Data Analysis: Pendulum Bob => 196.7 g ± 0.05 g = .1967 kg Uncertainty: (± 1.0 s) λ Mass N t
1.0 m .1967 kg 20 cycles 41.22 s 0.8 m .1967 kg 20 cycles 36.26 s 0.6 m .1967 kg 20 cycles 30.97 s 0.4 m .1967 kg 20 cycles 25.17 s 0.2 m .1967 kg 20 cycles 16.65 s - Keep d the same (initial sideways displacement) @ 30º Spring λ Mass N t (± 1.0 s) d (Vary it) 1.0 m .1967 kg 20 cycles 40.79 s 45º 1.0 m .1967 kg 20 cycles 41.63 s 25º 1.0 m .1967 kg 20 cycles 41.95 s 10º 1.0 m .1967 kg 20 cycles 40.57 s 50º
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- The uncertainty was estimated to be 1.0 s based on the students' reaction time to start and stop the stop watch.
x (± .005m) m (± .0005 kg) F 1. X 0 = 8 cm (.08 m) .05 kg (no mass added) 0.4905 N 2. X 0 = 12.2 cm (.122 m) .06 kg 0.5886 N 3. X 0 = 19.0 cm (.190 m) .08 kg 0.7848 N 4. X 0 = 25.5 cm (.255 m) .10 kg 0.981 N 5. X 0 = 32.8 cm (.328 m) .12 kg 1.1772 N Slope => m = 0.355 ± 0.063 y = mx + b b = -0.0908 ± 0.0053 r = 1.000 Questions: Pendulum 1. 41.22 s / 20 cycles = 2.061 t 2. 36.26 s / 20 cycles = 1.813 t
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3. 30.97 s / 20 cycles = 1.5485 t 4. 25.17 s / 20 cycles = 1.2585 t 5. 16.65 s / 20 cycles = 0.8325 t Spring 1. 40.79 s / 20 cycles = 2.0395 t 2. 41.63 s / 20 cycles = 2.0815 t 3. 41.95 s / 20 cycles = 2.0975 t 4. 40.57 s / 20 cycles = 2.0285 t - The source of the largest uncertainty was human er- ror in using the stopwatch, as well as when letting go of the mass to start the pendulum. - Recording the time for a large number of periods has a beneficial effect on the uncertainty since the best approach to reduce error is to time a large number of cycles (rather than trying to time one cycle perfectly). Conclusion: In conclusion, the students observed correlations between λ and t while performing the lab procedure and utilizing the Cap- stone program. The initial sideways displacement and t also have relationships, which the students discovered after running the Cap- stone software. To obtain the most reliable data, I discovered that it was essential to include as many trials as possible. I am satisfied with the findings of the numerous trials, and further investigation after the experiment has led me to the conclusion that human error had the greatest impact on the uncertainty factor.

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