Table of Contents
Unit: The Period of a Pendulum (Potential energy diagrams and integrated lab)
Potential energy diagrams (50 minutes)
Pendulum lab (50 minutes)
Pendulum period calculation (110 minutes)
Unit: Representing Harmonic Motion
Real representations (30 minutes)
Complex representations (70 minutes)
The simple harmonic oscillator (50 minutes)
Unit: Damped Harmonic Motion
The underdamped oscillator (50 minutes)
Unit: Driven Harmonic Oscillator, Fourier Series & Resonance
Single-Frequency Sinusoidal Driving Force (150 minutes)
Building & deconstructing periodic functions (xx minutes)
Unit: Response to an Impulse & a Simple Fourier Integral
Response to an impulse & a simple Fourier integral (xx minutes)
Unit: The Period of a Pendulum (Potential energy diagrams and integrated lab)
Potential energy diagrams (50 minutes)
Prerequisite Ideas
Potential energy diagrams
(Lecture, 50 minutes)
Energy Diagram Analysis
(Small Group Activity, 15 minutes)
Homework
Pendulum lab (50 minutes)
Prerequisite Ideas
Pendulum Lab
(Integrated Lab Activity, 50 minutes)
Homework
Pendulum period calculation (110 minutes)
Prerequisite Ideas
Calculation of Pendulum Period (Numerical Approach)
(Group problem solving activity, 50 minutes) (alternative a)
Calculation of Pendulum Period (Power Series Approach)
(Group problem solving activity, 50 minutes) (alternative b)
Homework
Unit: Representing Harmonic Motion
Real representations (30 minutes)
Prerequisite Ideas
Amplitude/phase and sine-plus-cosine
(Lecture, 15 minutes)
Initial conditions
(Group Activity, 15 minutes)
Homework
Complex representations (70 minutes)
Prerequisite Ideas
Review complex numbers & Euler
(Lecture, 40 minutes)
Complex representations; Initial conditions revisited
(Lecture, 20 minutes)
Homework
The simple harmonic oscillator (50 minutes)
Prerequisite Ideas
Simple pendulum from Newton's Law
(Lecture, 50 minutes)
Homework
Unit: Damped Harmonic Motion
The underdamped oscillator (50 minutes)
Prerequisite Ideas
Underdamped oscillator
(Lecture, 50 minutes)
Homework
Unit: Driven Harmonic Oscillator, Fourier Series & Resonance
Single-Frequency Sinusoidal Driving Force (150 minutes)
Prerequisite Ideas
Harmonic LRC Lab
(Integrated Lab Activity, 70 minutes)
Response of LRC circuit to sinusoidal driving force
(Lecture, 30 minutes)
Lab analysis, Admittance, impedance, resonance
(Discussion & Lecture, 40 minutes)
Three sinusoidal driving forces
(Group Activity, 10 minutes)
Homework
Building & deconstructing periodic functions (xx minutes)
Prerequisite Ideas
Guessing the Fourier Expansion of a Function
(Group Activity, 15 minutes)
Products of harmonic functions & projections
(Group Activity, xx minutes)
Fourier coefficients
(Lecture, xx minutes)
Fourier coefficients of a piecewise periodic function
(Group Activity, 40 minutes)
Homework
Unit: Response to an Impulse & a Simple Fourier Integral
Response to an impulse & a simple Fourier integral (xx minutes)
Prerequisite Ideas
The impulse function
(Lecture, xx minutes)
Impulse LRC Lab
(Integrated Lab Activity, 20 minutes)
Fast Fourier transform
Fourier transform example
(Lecture, xx minutes)
Homework