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lab 11damped oscillations 83 out of 85

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PHY 122

Lab 11: Damped Oscillations T.A: Monday at 2:00 p.m Abstract: This experiment was done in order to determine the effects amplitude, length and damping have on the motion of a pendulum. For part one, a tennis ball was attached to varying lengths of string and the period of motion for ten oscillations was found. For part two, the period of ten oscillations for varying amplitudes of the tennis ball pendulum were found. For part three, the motion of a Styrofoam ball pendulum was recorded for two minutes. From part one, an experimental value for the acceleration of gravity was found to be 12.5 +/- .1 m/s^2. Although that value is much larger than anticipated, the error was largely due to human error in the recording with the stopwatch. For part two, by graphing the amplitude versus the period there was no correlation found as the slope was close to zero (.003 +/- .002 sec/deg). For part three the values of τ, w, Q, and f were approximated by looking at the graph and the estimates were compared to the values given by the linear fit ( .8 versus .73 Hz for frequency, 5.026 versus 4.58 rad/sec for w, 40 versus 43 seconds for τ and 201.04 versus 199.55 radians for Q). Since the results were very similar, it was determined that both methods were acceptable but the method relying on the linear fit was suggested as the error was much less for the linear fit estimates. Overall the objectives of this lab were met despite human error with recording of the period. Objective: Examine how period varies with pendulum length and amplitude and to analyze how the motion is affected by damping. Equipment: The equipment used in this experiment was a tennis ball and a Styrofoam ball set up as a pendulum with varying lengths for the string. For parts one and two, a stopwatch was used to record the period and Data Analysis was used to record the results. A sonar detector was used for part three to record the period over two minutes. Procedure: First, the diameter and mass of the tennis ball and Styrofoam ball were recorded. For part 1, the period of ten oscillations were found for varying lengths of string for the tennis ball using amplitude less than .1 radians. For part 2, the period of ten oscillations for five different amplitudes, between five and twenty degrees, for the tennis ball was found. For part 3, two minutes of motion with the Styrofoam ball of a length of near sixty centimeters and amplitude of less than eleven degrees was recorded using a sonar detector. Results: Part 2 Theoretical Value for Gravity Actual value 12.5 +/- .1 m/s^2 9.81 m/s^2 Eyeball Actual Value Approximation f .8 Hz .73 Hz ω 5.026 rad/sec 4.58 rad/sec 40 seconds 43.57 τ seconds Q 201.04 rad 199.55 rad Data Analysis: Part 1: T=2∗π L T =4∗π ∗L/G T vs.L=¿ π 2 4∗π ¿/G √ G   (4* *L/G) *1/L  slope = ( 2 4∗π  G= slope Part 3: Approximated f by counting the number of oscillations in the first 10 seconds. Approximated τ by finding the time it took for the graph to decay to e^(-1) times its maximum −1 value. The maximum amplitude was .14 so to find τ, e ∗.14 was found to be roughly .5 and the x-coordinate corresponding to that value was roughly 40 seconds. A e−x/sin⁡(cx+d) The oscillatory fit equation found from the graph was The value obtained for c is equal to the value of , so ω= 4.58 rad/sec. The value of b is equivalent to τ, so τ=43.57 sec.
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