The Simple Pendulum - Worksheet 010422

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Drexel University *

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Mechanical Engineering

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Dec 6, 2023

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Simple Pendulum Lab Worksheet PHYS 101 Complete the following exercises as a group and turn in a single document with the names of group members. Ben Nordeman _____________________ _____________________ _____________________ Show work and calculations. An Excel spreadsheet is recommended to compile data. Time Period and Length Measure the time period of your pendulum in the manner described in the lab manual. Make measurements for at least 3 values of l by tying the string at different lengths. Put your data in the table below. To reduce error in your measurements, allow the pendulum to make 5 complete swings (from starting point -> other side -> back to starting point is one complete swing). Measure the time it takes for five swings and then divide by 5 to get the time for a single period. l 1 = l 2 = l 3 = .50m .30cm .40cm T (s) T (s) T (s) Multiple trials 1.368 0.996 1.206 1.38 1.01 1.216 1.314 1.02 1.23 Average 1.354 1.0087 1.217 Using T values, plot l vs T 2 , as described in the lab manual. Add a trendline to your plot and take note of the slope in the trendline equation. 1

0.25 0.3 0.35 0.4 0.45 0.5 0.55 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 f(x) = 3.63 x Length(m) vs T^2(s) Length (m) T^2(s^2) Find the slope of the trendline? Slope = 3.6287 As described in the lab manual, this slope is theoretically (4 ? 2 / g ). Use the result for the slope to make an experimental prediction for g . g exp = 4pi^2/3.6287 = 10.8795 m/s^2 Given that g = 9.8 m/s 2 , how accurate is the prediction? from this experiment Report a percent error using the procedure outlined in the lab manual. Percent error = (10.8795 -9.81) /9.81 x 100% = 10.9% Knowing the uncertainties in the time and length measurements, it is possible to calculate the uncertainty in the experimental prediction for g exp . (See lab manual for details.) This uncertainty will be different for each string length. Calculate the uncertainty for each string length and report results.  g/g= sqrt(((2  T)/Tn)^2+(  l/l)^2)= sqrt(((2*0.01)/1.0087)^2+(0.001/.30)^2) = 0.01046 m  g/g= sqrt(((2  T)/Tn)^2+(  l/l)^2)= sqrt(((2*0.01)/1.217)^2+(0.001/.40)^2) = 0.00859 m  g/g= sqrt(((2  T)/Tn)^2+(  l/l)^2)= sqrt(((2*0.01)/1.354)^2+(0.001/.50)^2)= 0.00765 m Time Period vs. Amplitude Now investigate the relationship between amplitude or how far you’ve lifted the pendulum and period, T . Keeping the length of your pendulums fixed at 100cm (or any desired length), measure the period in the same manner as before, while varying the angle (x) that you’ve released the pendulum from. Measure T for various values of x . Enter data in the table below. 2

It is okay to not know the specific angle, simply chose a specific location to release the pendulum from for x1 and do a different angle/location for x2 and x3 X 1 X 2 X 3 String l .23 .20 .15 T 1.34 1.26 1.18 1.32 1.266 1.19 1.31 1.263 1.2 Average T 1.323 1.263 1.19 To determine if changing the amplitude had any effect on the period, plot x vs T and add a trendline with a trendline equation. 0.14 0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 1.1 1.15 1.2 1.25 1.3 1.35 f(x) = 1.64 x + 0.94 X vs T X ( m) T(s) Following the procedure in the lab manual, calculate the relative percent variation in the T measurements from your x vs T data. Show your work and report your result in the space below. Relative % variation =(1.376-1.323/1.376)x100% =3.8% Analysis Questions and Further Considerations: 1. How does the calculated uncertainty in g exp for the shortest and longest values of l compare to the percent error in g exp ? What does this suggest about how the length of the string affects the experimental prediction? Hint: Refer to the lab manual for a derivation of uncertainty in g. 3

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