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Resonance
95 topics across 6 chapters
Chapter 1
Core concepts of resonance (physics intuition)
1
Oscillators and natural frequency
2 subtopics
2
Simple harmonic motion (SHM): equation, solution, phase
3
Derive natural frequency from restoring forces (spring, pendulum small-angle)
4
Damping and quality factor (Q)
2 subtopics
5
Damping models: viscous, Coulomb, structural (hysteretic)
6
Q factor, bandwidth, ringdown time (time–frequency connection)
7
Driven response and energy transfer
2 subtopics
8
Forced oscillator steady-state solution and resonance condition
9
Power and energy in driven oscillators (why amplitude grows at resonance)
10
Resonance vs beats vs entrainment (how to tell them apart)
11
Nonlinear and parametric resonance
2 subtopics
12
Duffing oscillator: hardening/softening spring and jump phenomenon
13
Parametric resonance (Mathieu equation intuition: pumping at 2f₀, etc.)
Chapter 2
Mathematical tools for resonance analysis
14
Complex numbers, phasors, and impedance-style reasoning
2 subtopics
15
Euler’s formula and rotating-vector picture (phasor intuition)
16
Mechanical–electrical analogies (impedance/mobility analogs)
17
Differential equations and Laplace/transfer functions
2 subtopics
18
Solve the standard 2nd-order ODE (under/critical/overdamped)
19
Build transfer functions; poles/zeros interpretation for resonant systems
20
Frequency response and Bode plots (magnitude/phase)
2 subtopics
21
Resonant peak, -3 dB points, bandwidth, and Q from Bode plots
22
Phase lag near resonance and its physical meaning (energy flow, stability)
23
Fourier transform and spectra (what resonance looks like in frequency domain)
2 subtopics
24
FFT in practice: sampling rate, resolution, interpreting peaks
25
Spectral leakage, windowing, and averaging for resonance measurements
26
Eigenvalues, eigenmodes, and coupled oscillators
2 subtopics
27
Two coupled oscillators: normal modes and mode splitting
28
Modal superposition basics (why multiple resonances appear)
Chapter 3
Mechanical resonance and vibration
29
Single-degree-of-freedom (SDOF) vibration systems
2 subtopics
30
Mass–spring–damper experiment: measure f₀, ζ, Q from data
31
Rotating imbalance and critical speeds (machinery resonance)
32
Multi-degree-of-freedom structures (beams, frames, plates)
2 subtopics
33
Beam/plate resonances: boundary conditions and mode families
34
Mode shapes, nodes/antinodes, and why placement matters
35
Vibration isolation and tuned absorbers
2 subtopics
36
Tuned mass damper (TMD): choosing mass ratio, tuning, damping
37
Base excitation transmissibility curve and isolation region
38
Resonance failures and robust design
2 subtopics
39
Case study: Tacoma Narrows and aeroelastic resonance/instability
40
Resonance-avoidance checklist: detuning, damping, load paths, fatigue
Chapter 4
Electrical resonance (circuits, RF, crystals)
↗ Complex numbers, phasors, and impedance-style reasoning (see Chapter 2)
41
RLC resonance fundamentals (series and parallel)
2 subtopics
42
Series vs parallel resonance: impedance curves and practical meaning
43
Q and bandwidth in RLC: losses, ESR, and loading effects
44
Filters and impedance matching around resonance
2 subtopics
45
Design band-pass and notch filters from a resonance target
46
Impedance matching basics near resonance (why mismatch shifts Q/f₀)
47
RF and microwave resonators
2 subtopics
48
Cavity/dielectric resonators and resonant frequency setting
49
Measure RF resonators with S-parameters (S11/S21) and extract Q
50
Oscillators: using resonators to set frequency
2 subtopics
51
Barkhausen criterion and loop-gain view of oscillation start-up
52
Resonator-in-loop: phase noise intuition and why higher Q helps
53
Piezoelectric and crystal resonators (electromechanical resonance)
2 subtopics
54
Piezo equivalent circuits (motional branch) and anti-resonance
55
Quartz crystal basics: load capacitance, drive level, pulling
Chapter 5
Resonance in waves: acoustics, optics, quantum, antennas
56
Standing waves and boundary conditions
2 subtopics
57
Harmonics, resonance series, and mode numbering (n=1,2,3,…)
58
Strings and air columns: fixed/free ends and resonance frequencies
59
Acoustic resonance in air and structures
2 subtopics
60
Room modes and practical measurement (why bass builds up in corners)
61
Helmholtz resonator: bottle model, tuning, and bandwidth
62
Optical resonances
2 subtopics
63
Fabry–Pérot: free spectral range, linewidth, finesse
64
Ring/whispering-gallery resonators: coupling and loaded vs intrinsic Q
65
Quantum/atomic resonance (transitions and driven systems)
2 subtopics
66
Driven two-level system and Rabi oscillations (conceptual level)
67
NMR/ESR resonance condition (Larmor frequency) and what’s measured
68
Waveguides, cavities, and antenna resonance
2 subtopics
69
Quarter-wave and half-wave resonators in transmission lines
70
Antenna resonance and matching: what “resonant” means for antennas
Chapter 6
Measurement, modeling, and engineering practice
↗ Frequency response and Bode plots (magnitude/phase) (see Chapter 2)
71
System identification for resonant systems
2 subtopics
72
Test inputs: swept-sine vs chirp vs impulse; when to use each
73
Fit an FRF to estimate f₀, damping ratio ζ, and Q (hands-on workflow)
74
Experimental modal analysis (EMA)
2 subtopics
75
Impact-hammer testing: coherence, averaging, and common pitfalls
76
Sensors for resonance: accelerometers, microphones, laser vibrometry
77
Damping treatments and materials
2 subtopics
78
Viscoelastic damping layers and constrained-layer damping (CLD) basics
79
Fluid damping and dashpots: modeling and limitations
80
Control of resonance (passive and active)
2 subtopics
81
Notch filters and input shaping to suppress resonant excitation
82
Feedback control and resonance: avoiding excitation and instability
83
Numerical simulation tools (FEM/SPICE)
2 subtopics
84
FEM eigenfrequency study: mesh/boundary-condition sensitivity checklist
85
SPICE AC analysis of resonant circuits: extracting f₀ and Q under load
86
Safety, troubleshooting, and mitigation in real systems
2 subtopics
87
Resonance troubleshooting checklist (symptoms → measurements → fixes)
88
Design review for resonance risk: documentation, margins, and sign-off

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