Unit II: Second Order Constant Coefficient Linear Equations · Lecture Videos

Constant Coefficient Second Order Homogeneous DE's

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Unit II: Second Order Constant Coefficient Linear Equations · Lecture Videos

Real Roots: Overdamping

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Unit II: Second Order Constant Coefficient Linear Equations · Lecture Videos

Complex Roots: Underdamping

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Unit II: Second Order Constant Coefficient Linear Equations · Lecture Videos

Repeated Roots: Critical Damping

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Unit II: Second Order Constant Coefficient Linear Equations · Lecture Videos

Real Solutions from Complex Roots

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Unit II: Second Order Constant Coefficient Linear Equations · Problem-solving Videos

Homogeneous Constant Coefficient Equations: Real Roots

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Unit II: Second Order Constant Coefficient Linear Equations · Problem-solving Videos

Homogeneous Constant Coefficient Equations: Any Roots

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Unit II: Second Order Constant Coefficient Linear Equations · Lecture Videos

Damping and Pseudo-Frequency

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Unit II: Second Order Constant Coefficient Linear Equations · Demonstration Videos

Exploration of the Damped Vibrations Applet

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Unit II: Second Order Constant Coefficient Linear Equations · Problem-solving Videos

Damped Harmonic Oscillators

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Unit II: Second Order Constant Coefficient Linear Equations · Lecture Videos

Linear Operators and Superposition

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Unit II: Second Order Constant Coefficient Linear Equations · Lecture Videos

Inhomogeneous Second Order DE's: Definitions and Models

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Unit II: Second Order Constant Coefficient Linear Equations · Lecture Videos

Particular and General Solutions

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Unit II: Second Order Constant Coefficient Linear Equations · Lecture Videos

Inhomogeneous DE's with Exponential Input

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Unit II: Second Order Constant Coefficient Linear Equations · Problem-solving Videos

Forced Oscillations

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Unit II: Second Order Constant Coefficient Linear Equations · Lecture Videos

Definition of Stability

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Unit II: Second Order Constant Coefficient Linear Equations · Lecture Videos

Stability of Constant Coefficient Second Order DE's

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Unit II: Second Order Constant Coefficient Linear Equations · Problem-solving Videos

Gain and Phase Lag

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Unit II: Second Order Constant Coefficient Linear Equations · Problem-solving Videos

Undetermined Coefficients

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Unit II: Second Order Constant Coefficient Linear Equations · Lecture Videos

Solving DE's with Exponential Input when p(a) = 0

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Unit II: Second Order Constant Coefficient Linear Equations · Lecture Videos

Resonance in the Undamped System

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Unit II: Second Order Constant Coefficient Linear Equations · Lecture Videos

Reconciling the Resonant and Non-resonant Solutions

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Unit II: Second Order Constant Coefficient Linear Equations · Problem-solving Videos

Pure Resonance

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Unit II: Second Order Constant Coefficient Linear Equations · Demonstration Videos

Exploration of the Amplitude and Phase: Second Order II Applet

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Unit II: Second Order Constant Coefficient Linear Equations · Problem-solving Videos

Frequency Response

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Differential Equations — Unit II: Second Order Constant Coefficient Linear Equations

Materials by section

Characteristic Equation

Damped Oscillators

Exponential Response

Gain and Phase Lag

Undetermined Coefficients

Linear Operators

Pure Resonance

Frequency Response

Applications

Exam 2

Constant Coefficient Second Order Homogeneous DE's

Real Roots: Overdamping

Complex Roots: Underdamping

Repeated Roots: Critical Damping

Real Solutions from Complex Roots

Homogeneous Constant Coefficient Equations: Real Roots

Homogeneous Constant Coefficient Equations: Any Roots

Damping and Pseudo-Frequency

Exploration of the Damped Vibrations Applet

Damped Harmonic Oscillators

Linear Operators and Superposition

Inhomogeneous Second Order DE's: Definitions and Models

Particular and General Solutions

Inhomogeneous DE's with Exponential Input

Forced Oscillations

Definition of Stability

Stability of Constant Coefficient Second Order DE's

Gain and Phase Lag

Undetermined Coefficients

Solving DE's with Exponential Input when p(a) = 0

Resonance in the Undamped System

Reconciling the Resonant and Non-resonant Solutions

Pure Resonance

Exploration of the Amplitude and Phase: Second Order II Applet

Frequency Response