ECExplain

Contents

Control Systems
Introduction
Open Loop SystemsClosed Loop SystemsControl System ComponentsTransfer FunctionBlock Diagram BasicsBlock Diagram ReductionSignal Flow Graph ConstructionMason Gain Formula
Time Domain Analysis
Test Input SignalsFirst Order System ResponseSecond Order System ParametersSecond Order Underdamped ResponseSecond Order Overdamped ResponseSecond Order Critically Damped ResponseTime Domain SpecificationsSystem Type NumberSteady State ErrorSteady State Error ImprovementDominant Poles
Stability Analysis
BIBO StabilityRouth-Hurwitz CriterionRouth Array Special Case Zero ElementRouth Array Special Case Zero RowRoot Locus ConceptRoot Locus Construction RulesRoot Locus Breakaway PointsRoot Locus Angle of DepartureRoot Locus and StabilityComplementary Root Locus
Frequency Response
Frequency Response ConceptBode Plot ConstructionBode Plot of First Order SystemBode Plot of Second Order SystemGain MarginPhase MarginGain and Phase Margin from BodePolar PlotNyquist Plot ConstructionNyquist Stability CriterionNichols ChartAll Pass and Minimum Phase Systems
Compensators
Lead Compensator DesignLag Compensator DesignLead-Lag CompensatorP ControllerPI ControllerPD ControllerPID ControllerZiegler-Nichols Tuning
State Space
State VariablesState Space RepresentationState Space from Transfer FunctionTransfer Function from State SpaceState Transition MatrixControllabilityObservabilityState Feedback ControlObserver DesignDiagonalization
Digital Control
Sampled Data SystemsZ-Domain AnalysisDigital PID ControllerStability in Z-DomainBilinear Transformation w-domain
Other Topics
Other Subjects
Analog ElectronicsDigital ElectronicsSignals & SystemsElectromagnetic TheoryDigital CommunicationAnalog CommunicationNetwork AnalysisMicroprocessorsVLSI DesignVerilog HDLPower ElectronicsEmbedded SystemsDSPElectronic Devices
Section Progress33%

4 of 12 articles

Bode Plot of Second Order System

Resonant peak, damping effect on magnitude.

Mohith N
Updated: 19 March 2026
5 min read
#Control Systems

Second Order Bode Quiz

Test your understanding of resonant peaks, damping ratio effects, and Bode plots for second-order systems.

Question 1 of 3

Q1.For a standard second-order system G(s) = wn^2 / (s^2 + 2*zeta*wn*s + wn^2), the resonant peak in the Bode magnitude plot occurs at the resonant frequency wr. What is wr?

Related Articles

Bode Plot Construction

Magnitude in dB and phase plots, asymptotic approximation.

7 min read

Second Order System Parameters

Damping ratio zeta, natural frequency wn, categories.

9 min read

Gain and Phase Margin from Bode

Reading margins from Bode plot, stability.

12 min read

Second Order Underdamped Response

Oscillatory, overshoot, peak time, settling time.

11 min read

Second Order Overdamped Response

No oscillation, sum of exponentials, slow response.

8 min read

Previous
Bode Plot of First Order System
Next
Gain Margin