Resonance and Frequency Response Essay examples

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ME 3057 - EXPERIMENTAL METHODOLOGY & TECHNICAL WRITING
Report: Lab number 3
Full Report: X Partial Report:
Lab section: H

Grader: _____________

NAMES : Kyle Reno, Chantly Smith

Date Turned In: 9/20/07

Date Returned by TA: ____________________

The effort / participation in this laboratory and lab report is divided as follows:
Name: Chantly Smith, primarily responsible for sections:
Experimental Results/Analysis
Name: Kyle Reno, primarily responsible for sections:
Conclusion

Abstract,

Experimental

Objective,

Results/Analysis,

Procedure,

Discussion,

By submitting this lab report electronically, I/we are agreeing to the following honor pledge, which is consistent with the rules described in the laboratory manual, the syllabus and in class:
On my honor, I / we pledge that I / we have neither given nor received inappropriate aide in the preparation of this lab report. The only laboratory reports from prior semesters that I / we have viewed, reviewed, or used in any way were provided by the laboratory TAs during office hours. I / we have reviewed the consequences of using prior laboratory reports in the laboratory manual.

GRADE:

/

COMMENTS (grader / students)

Grader Initials: ________

ABSTRACT
The goal of this lab was to compare theoretical models of second order mechanical systems to experimental data. The dynamics of second order mechanical systems is an important consideration in a wide variety of engineering fields. Automobiles, for instance, contain a number of parts that can be represented as spring-damper systems. The ability of such systems to return to their equilibrium conditions as well as the dangers of oscillating input forces create important design considerations. A second order system may be fully characterized by its natural frequency and damping ratio. The primary objective of this experiment was to characterize a second order system using two distinct experimental methods. A system was characterized for both a low and high damping factor. The first characterization method involved observing the time response of the system to an initial displacement from its equilibrium position. This method found that the damping ratio of the system was 0.078 for high damping with a natural frequency of oscillation of 15.4 rad/s. The second method observed the response of the system to harmonic displacement inputs of varying frequencies. Based on the input frequency, the output could be expressed by a gain and phase shift from the input. This method yielded a damping ratio of 0.162 and natural frequency of oscillation of 20.6 rad/s for the high damping factor. These natural frequencies were compared to the theoretical natural frequency, which was determined to be 14.9 rad/s. The time response method yielded results that were closer in agreement with theory. The report concludes that the time response method is more reliable for characterizing systems due to somewhat arbitrary frequency values that the measurements were taken at for the frequency response method.

ME3057, Fall 2007

OBJECTIVE
The objectives of this experiment are to compare measured results to theory for second order mechanical systems and to compare the time response and frequency response methods of characterizing these systems. The second order system analyzed in this report was a spring-massdamper system.

PROCEDURE
Before the experiment could be conducted, the oscilloscope’s display needed to be calibrated to relate the voltages to the displacements of the base and the mass. To perform the calibration, weights of varying mass were individually placed on the system, and the displacement change and output voltage were recorded between each additional mass. A linear regression line was made from the displacement and mass data in order to determine the spring constant. To observe the time response to a step input, the spring-mass-damper system was pulled down as far as possible and released so
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