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California State University, Long Beach *

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1510

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Mechanical Engineering

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Apr 3, 2024

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Lab: Simple Harmonic Motion Simple Harmonic Motion Part A: Spring in Static Equilibrium Table 1: Elongation of a Coil Spring in Static Equilibrium for Various Masses Mass added to spring, M (kg) Distance above floor, d ( ) Elongation, x (m) Suspended weight, Mg ( ) 0 0.00 --------------- 0.100 0.200 0.300 0.400 0.500 Calculations: Show the following two calculations for 0.500 kg added to the spring . Use SI units and include them in the calculation, as always. As always, show WORK. • Elongation of the spring, x = • Suspended weight, Mg = Part B: Oscillating Spring Mass of spring, m s (kg): Table 2: Average Periods for Various Suspended Masses on an Oscillating Coil Spring Suspended Mass, m (kg) Total time for 30 oscillations, t (s) Period (time for one oscillation), T (s) Period Squared, T 2 (s 2 ) 0.100 0.200 0.300 0.400 0.500 Calculation: Show the calculation of the [average] period of oscillation from the total time, T , for 0.500 kg suspended mass . Include units and show work, as always. Period, T = M N 1.451 1.545 0.106 0.981 1.445 0.204 1.962 1.350 0.301 2.943 1.235 0.414 3.924 1.130 0.521 4.905 1.651m-1.130m = 0.521m (0.981) (0.500) 4.905N 0. 1767 24.3 0.47 0.4.5 30.78 0.95 8.90 35.94 1.1 1.35 40.75 1.34 1.80 45.13 1.50 2.25 IT = 1.50 k = m 440.500) = 8.72 (1.SOn2

Lab: Simple Harmonic Motion Graph 1 – Computer : Plot Mg vs. x (Suspended weight vs. elongation) for Part A data using LineFit ( https://www.cpp.edu/~pbsiegel/javascript/linefitjs.html ), screenshot the graph from LineFit to include the graph and the values of the slope and the y-intercept with their uncertainties. Graph 2 – Computer : Plot a graph of T 2 vs. m (Period squared vs. suspended mass) for Part B data using LineFit ( https://www.cpp.edu/~pbsiegel/javascript/linefitjs.html ), screenshot the graph from LineFit to include the graph and the values of the slope and the y-intercept with their uncertainties. (See the “Example” at the end of the Lab 2 assignment sheet for an example of a plot worth full points in a lab report!). Table 3: Spring Constant and Oscillating Mass from the Spring-Mass System Plot Slope Spring Constant, k ( ) x -intercept measured off graph ( ) Mass of oscillating part of spring, m o ( ) Value Units Mg vs. x k A = T 2 vs. m k B = Calculation: Show the calculation of the spring constant, k, from the slope of the T 2 vs. m best fit line (Part B graph). Include units. Show work. • Spring constant, k = Questions: 1. (a) Look at your part A graph: Does the spring obey Hooke’s law? Yes No (b) What about your part A graph tells you this? There is no conclusion paragraph for this lab report. N/M 9.45 = 1.05 N/m 4.17 m kg 4.50 = 4.0S S"/ kg 8.77 0 0.17 4.50 = x = 0 = = 8. Nim x 1100 =-0 k = A 4.1 0 Graph A obeys Hooke's law because as the elongation increases, so does the weight and force.