Differential Equations

Exponential Input; Gain and Phase Lag

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Session Overview

In this session we will study the special case of a linear first order constant coefficient with the input function an exponential. Converting sinusoids to complex exponentials will allow us to handle the very important case of sinusoidal input.

Session Activities

Read the course notes:

• Exponential Input; Gain and Phase Lag: Introduction (PDF)
• First Order Response to Exponential Input (PDF)
• First Order Response to Sinusoidal Input (PDF)
• Amplitude Phase, Gain and Bode Plots (PDF)

Learn from the Mathlet materials:

• Watch the video Exploration of the Amplitude and Phase: First Order Applet
• Work with the Amplitude and Phase: First Order Applet

Watch the problem solving video:

• Sinusoidal Inputs

Complete the practice problems:

• Practice Problems 8 (PDF)
• Practice Problems 8 Solutions (PDF)

Check Yourself

Complete the problem sets:

• Problem Set Part I Problems (PDF)

• Problem Set Part I Solutions (PDF)

• Problem Set Part II Problems (PDF)

• Problem Set Part II Solutions (PDF)

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