Session Overview
 | In this session we will add input to our differential equations. In particular, we will look at constant coefficient linear equations with exponential input. Because of Euler's formula we will be able to use this and complex arithmetic to include the key case of sinusoidal input. |
Session Activities
Read the course notes:
Watch the lecture video clip:
- Linear Operators and Superposition (00:16:51)
Read the course notes:
Watch the lecture video clips:
-
Inhomogeneous Second Order DE's: Definitions and Models (00:16:26)
Inhomogeneous Second Order DE's: Definitions and Models
> Download from iTunes U (MP4 - 88MB)
> Download from Internet Archive (MP4 - 88MB)
- Particular and General Solutions (00:10:17)
-
Inhomogeneous DE's with Exponential Input (00:24:52)
Inhomogeneous DE's with Exponential Input
> Download from iTunes U (MP4 - 91MB)
> Download from Internet Archive (MP4 - 91MB)
Read the course notes:
- Exponential Input (PDF)
- Sinusoidal Input (PDF)
- The Simple Harmonic Oscillator (PDF)
- Generalized Exponential Response Formula (PDF)
Complete the practice problem:
Watch the problem solving video:
- Forced Oscillations (00:13:06)
Complete the practice problems:
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)