The Experimental Mechanics and Dynamic System Analysis Lab offered an in-depth exploration of vibration analysis, system dynamics, and frequency response characterization, supported by hands-on lab experiments involving mechanical oscillations, coupled system behavior, and electrochemical impedance spectroscopy. Each experiment ranged from studying simple pendulum motion to analyzing complex two-degree-of-freedom systems and electrical impedance models, and I gathered data, applied MATLAB-based signal processing, and compared theoretical predictions to observed behavior. These experiences also involved dynamic signal sampling, frequency analysis, and system identification using MATLAB and Simulink, shedding light on free and forced vibrations and revealing how real-world systems respond to various conditions. This comprehensive approach reinforced my understanding of mechanical vibrations, system dynamics, and signal processing, which are crucial skills for fields such as robotics, aerospace, and structural engineering.
This lab validated the Nyquist-Shannon Sampling Theorem by examining how sampling rates and aliasing affect both the time-domain waveform and frequency-domain representation. Using tuning forks at different frequencies, I explored how real-world mechanical signals are acquired and processed, ensuring that the sampling frequency is at least twice the highest frequency present in the signal.
Key Takeaways:
Lower sampling rates produced distorted waveforms and incorrect frequency content due to aliasing, highlighting the importance of choosing appropriate sampling frequencies
Sampling rate selection is critical in dynamic systems to avoid aliasing and data distortion
The Fast Fourier Transform (FFT) allowed for precise analysis of frequency components, and MATLAB’s frequency-domain visualization helped confirm theoretical predictions
Higher sampling rates improved signal reconstruction accuracy and ensured high-fidelity data collection
This experiment focused on the motion of single and double pendulum systems, contrasting theoretical oscillation models with real-world behavior. The double pendulum demonstrated chaotic motion, where small changes in initial conditions caused significantly different outcomes. High-speed imaging and MATLAB scripts were used to track motion and convert pixel coordinates into physical measurements.
Key Takeaways:
Small-angle oscillations in a simple pendulum followed harmonic motion equations, while larger angles showed nonlinear effects
The double pendulum is highly sensitive to initial conditions, making it a classic example of chaotic motion
Image processing techniques in MATLAB provided accurate motion tracking and enabled comparisons with theoretical models
In this lab, I examined a spring-mass-damper system under free oscillations. By analyzing how damping ratios and natural frequencies influence the system, I confirmed the accuracy of the damped harmonic motion model through experimental measurements.
Key Takeaways:
Underdamped systems continued to oscillate before settling, while higher damping caused rapid decay in motion
The experimental damping ratio closely matched theoretical values, validating damped harmonic motion equations
Laplace transforms and MATLAB simulations confirmed that the natural frequency and damping ratio dictate system behavior
Building on the free response lab, this experiment introduced harmonic excitation, where external forces were applied at varying frequencies. By measuring the system’s amplitude and phase response, I identified resonance conditions and examined how damping affects forced vibrations.
Key Takeaways:
Resonance occurred near the system’s natural frequency, where oscillations reached their peak amplitude
Bode plots illustrated the relationship between frequency and system gain, revealing how damping becomes more pronounced at higher frequencies
MATLAB simulations and experimental data showed strong agreement, reinforcing theoretical models of forced vibration
This lab explored a coupled mechanical system where a pendulum was attached to a moving cart, representing a fundamental model for multi-degree-of-freedom dynamics. By analyzing both free and forced responses, I investigated how natural frequencies and mode shapes influence system behavior. This setup also introduced basic control concepts, including system identification and potential stabilization strategies.
Key Takeaways:
Coupled systems exhibit multiple natural frequencies and complex mode shapes, requiring modal analysis to predict responses
Resonance occurred near the system’s primary natural frequency, significantly amplifying the cart’s displacement
The pendulum displayed nonlinear behavior at larger displacements, deviating from simple harmonic approximations
System identification techniques, along with MATLAB and Simulink simulations, provided valuable insights into physical parameters and potential control approaches
In this experiment, I applied EIS to a resistor-capacitor (RC) circuit, analyzing frequency-dependent impedance behavior. By generating Bode and Nyquist plots, I examined transitions from resistive to capacitive behavior and compared experimental results to theoretical predictions. Simulink and Simscape models offered real-time simulations that closely matched the measured data.
Key Takeaways:
Impedance decreases with increasing frequency, transitioning from resistive to capacitive behavior in an RC circuit
Bode plots and Nyquist plots visualized how phase and magnitude change over frequency
Theoretical models accurately predicted circuit behavior, and MATLAB-based simulations confirmed experimental observations
Expanding on the previous EIS work, this lab involved multiple RC circuits arranged in series and parallel, creating a more complex impedance network. By studying interactions between these components, I gained a deeper understanding of how frequency-dependent effects influence circuit performance in practical applications.
Key Takeaways:
Series RC circuits followed additive rules, while parallel configurations introduced nonlinear interactions
Parasitic effects and component tolerances became more significant at higher frequencies, causing measurement discrepancies
Theoretical impedance models remained valid across a wide range of frequencies, reinforcing the importance of careful circuit design and accurate frequency-domain analysis
These labs provided practical experience in validating theoretical models and understanding the real-world dynamics of mechanical and electrical systems. Key lessons included the importance of proper sampling rates to avoid aliasing, the impact of nonlinearities and chaotic motion, and the need to account for resonance and damping in system design. EIS further demonstrated how frequency-dependent behavior shapes circuit performance, highlighting the role of precise modeling and measurement techniques.