Table of ContentsList of Figures and TablesExecutive Summary1. Introduction2. System Analysis2.1 Basic Concepts2.2 Spring-Mass Theory2.3 Damper-Mass Theory2.4 Spring-Damper-Mass Theory3. Apparatus4. Procedure5. Results5.1 Static Spring Constant Calculation5.2 Analysis of Raw Kinetic Data5.3 Spring-Mass System5.4 Spring-Mass-Damper System6. Analysis and Interpretation6.1 Spring Constant Comparison6.2 Damping Coefficient Comparison6.3 Procedure Improvement7. Conclusions and RecommendationsGrand Valley State UniversityThe Padnos School of EngineeringBASIC SYSTEM COMPONENTSEGR 345 Dynamic Systems Modeling and ControlJoshua Hoekstra9/28/99Lab PartnerJoel OostdykFall 1999Table of ContentsTable of Contents_________________________________________________2List of Figures and Tables_________________________________________3Executive Summary_______________________________________________41. Introduction___________________________________________________52. System Analysis_______________________________________________52.1 Basic Concepts_______________________________________________________________52.2 Spring-Mass Theory___________________________________________________________62.3 Damper-Mass Theory__________________________________________________________72.4 Spring-Damper-Mass Theory____________________________________________________83. Apparatus_____________________________________________________94. Procedure____________________________________________________105. Results______________________________________________________115.1 Static Spring Constant Calculation_______________________________________________115.2 Analysis of Raw Kinetic Data___________________________________________________115.3 Spring-Mass System__________________________________________________________135.4 Spring-Mass-Damper System___________________________________________________136. Analysis and Interpretation______________________________________166.1 Spring Constant Comparison___________________________________________________166.2 Damping Coefficient Comparison_______________________________________________166.3 Procedure Improvement_______________________________________________________177. Conclusions and Recommendations______________________________17List of Figures and TablesTable 1 - List of Apparatus...................................................................................................9Table 2 – spring data..........................................................................................................13Table 3 – damping coefficients...........................................................................................15Figure 1. Spring-Mass System............................................................................................6Figure 2. Damper-Mass System..........................................................................................7Figure 3. Spring-Damper-Mass System..............................................................................8Figure 4 - The setup...........................................................................................................10Figure 5 – spring constant calculation................................................................................11Figure 6 – Example of raw data.........................................................................................12Figure 7 – damper 1, trial 1................................................................................................14Figure 8 – damper 1, trial 2................................................................................................14Figure 9 – damper 2, trial 1................................................................................................14Figure 10 – damper 2, trial 2..............................................................................................153Executive SummaryThe purpose of this lab was to examine the motion of two simple translational systems. The first system examined consisted of a spring and mass and the second system consisted of a spring, mass and damper. The second system was studied using two different dampers.In this lab the spring constant of a spring was determined statically and also kinetically, using an ultrasonic sensor. The damping coefficient of a damper was also calculated by studying its motion in a spring-mass damper system.The results of this lab showed a 1.52% error between the statically determined spring constant and the kinetically determined spring constant. The results of the damping coefficients were different than expected. It was expected that the damping coefficient of the second damper would be larger than the first damper, however, this was not the case. After some thought the reason for this was determined to be the flimsy plastic-damping piston used for damper 2. The large surface area dampened out any large initial motion, but because it was flimsy it was not able to dampen out any small motions. Also, there was a wide range of correlation that added to the uncertainty of the damping coefficient calculations.From this lab it was concluded that by studying the motion of different systems the coefficient values of the system components could be calculated. From this lab it can be said that the analytical model agrees with the observed behavior of the system within 11% with a confidence level of 85% for the conditions of this experiment.41. IntroductionThe purpose of this lab was to examine the motion of two simple translational systems. The first system that was examined consisted of a spring and mass and the second system consisted of a spring, mass and damper.The system composed of the spring and mass is a simple oscillating system that, underideal conditions, would oscillate forever. The motion of this system could be studied and from its motion the spring constant could be calculated.The system composed of the spring, mass and damper is an oscillating system that, under the conditions that the damping coefficient is not too large, would oscillate. However, with the damper attached to the system the oscillating motion would eventually be damped out and the motion of the system would stop. The motion of this system couldalso be studied and from its motion the damping coefficient could be calculated.In this lab concepts involved in these mechanical systems will be discussed. After understanding the concepts involved the