Analysis of lumped and distributed parameter systems. Concepts of torsional vibration. Resonances. Frequency response and transfer function methods. Modal analysis. Mathematical modeling using experimental data. Digital Fourier analysis and Fast Fourier Transform. Signal processing. Data acquisition. Data formats. Transducer measurement considerations. Vibration data processing and instrumentation. Typical vibration problems. Fault diagnosis techniques of rotating machinery. Basic balancing of rotors. Resonance and critical speed testing. Machine analysis case studies.