spring_mass_lab_report_sample
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School
Georgia Institute Of Technology *
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Course
2610
Subject
Aerospace Engineering
Date
Feb 20, 2024
Type
Pages
10
Uploaded by SargentDangerSwan38
AE 2610, Lab 3 Spring Mass Lab Report Lab Group A03-Y Fall, 2023
1 Introduction This experiment analyzes the linearized and nonlinearized responses of a spring mass damper system to an applied impulse. The spring mass damper system analyzed is a helicopter mechanism that has one degree of freedom. The helicopter mechanism consists of thrust generating equipment on one end of a beam and a counterweight on the other end. This Data Results Raw Data The raw data acquired includes the dimensions of the helicopter assembly as well as the masses associated with this assembly, which can be found in Table I. The voltages and the
2 associated settling angles were also measured and captured in Table III. The thrust associated Reduced Data The data reduction involved plotting the change in theta of the helicopter assembly against time to analyze the way the system responded to an impulse over time. This was Derivations Nonlinear equation of motion ! " = $%
(1) ! & = '(
̈
(2) ! " = −%&
̇
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3 ! & = −+,
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+ .$
!
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(6) Linearized equation of motion Applying the small angle assumption (
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4 Damping ratio and natural frequency in terms of model parameters From linearized equation of motion: =
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(12) Natural Frequency: =
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(13) (14) (15) Damping Ratio: @ =
(16) Predicted natural settling angle from thrust Using nonlinear equation:
5 Discussion
The empirically obtained and model parameter-predicted damping ratio and natural frequency match up somewhat well but not remarkably. One reason for this could be
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6 Tables and Figures Tables Table I. Dimensions and masses of the helicopter mechanism. Mass of Counterweight (m
CW
) Horizontal Displacement of Counterweight (l
CWx
) Vertical Displacement of Counterweight (l
CWy
) Mass of Thrust Generating Equipment (m
T
)
7 Table II. Predicted and measured damping ratios, natural frequencies, and leveling forces. Empirically Obtained Damping Ratio Model Parameter Predicted Damping Ratio Empirically Obtained Natural Frequency Model Parameter Predicted Natural Frequency Predicted Steady Level Hover Thrust Measured Leveling Force nd measured settling angles for various voltage inputs. Voltage Predicted Angle Measured Angle 0 2.5 5 7.5 10 Figures
8 Thrust=1.246V
2
-1.9958V+1.2906 Figure 1. Thrust of helicopter simulator plotted against voltage output to helicopter simulator. Figure 2. The linear impulse response of a spring mass damper system helicopter simulation showing the measured response, the manually adjusted response, and the model-parameter-
predicted response. 0
100
120
0
2
4
6
8
10
12
Thrust (g)
Voltage (V)
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9 Figure 3. The nonlinear impulse response of a spring mass damper system helicopter simulation showing the measured response, the manually adjusted response, and the model-parameter-
predicted response.