### Unit: The Period of a Pendulum (Potential energy diagrams and integrated lab)

#### Potential energy diagrams (50 minutes)

- Potential energy diagrams (Lecture, 50 minutes)
- Energy Diagram Analysis (Small Group Activity, 15 minutes)

#### Pendulum lab (50 minutes)

- Pendulum Lab (Integrated Lab Activity, 50 minutes)

#### Pendulum period calculation (110 minutes)

- 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)

### Unit: Representing Harmonic Motion

#### Real representations (30 minutes)

- Amplitude/phase and sine-plus-cosine (Lecture, 15 minutes)
- Initial conditions (Group Activity, 15 minutes)

#### Complex representations (70 minutes)

- Review complex numbers & Euler (Lecture, 40 minutes)
- Complex representations; Initial conditions revisited (Lecture, 20 minutes)

#### The simple harmonic oscillator (50 minutes)

- Simple pendulum from Newton's Law (Lecture, 50 minutes)

### Unit: Damped Harmonic Motion

#### The underdamped oscillator (50 minutes)

- Underdamped oscillator (Lecture, 50 minutes)

### Unit: Driven Harmonic Oscillator, Fourier Series & Resonance

#### Single-Frequency Sinusoidal Driving Force (150 minutes)

- 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)

#### Building & deconstructing periodic functions (xx minutes)

- 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)

### Unit: Response to an Impulse & a Simple Fourier Integral

#### Response to an impulse & a simple Fourier integral (xx minutes)

- The impulse function (Lecture, xx minutes)
- Impulse LRC Lab (Integrated Lab Activity, 20 minutes)
- Fast Fourier transform
- Fourier transform example (Lecture, xx minutes)