Paradigms in Physics: Oscillations and Waves | 2025-Spring

Course Name
Paradigms in Physics: Oscillations and Waves
Course Number
ph424
Year/Term
Spring-2025
Course Credits
4
Class meeting times
9 hours of lecture/discussion per week for five weeks.
Prerequisites
PH 335, MTH 256
Course description
Dynamics of mechanical and electrical oscillation using Fourier series and integrals; time and frequency representations for driven damped oscillators, resonance; one-dimensional waves in classical mechanics and electromagnetism; normal modes.
Topic/Day
Activities
Resources
Homework Due
W1 D1
Intro to Oscillations
Explore Canvas Site
Access Jeff's GoodNotes Notebook
Login to Gradescope
Euler's Formula (Review)
Euler's Formula Review
Orthonormality of Sines and Cosines
Inner Products of Sines and Cosines
Reading:
GMM: Fourier Basis Functions
GMM: Inner Products of Functions
The Kronecker Delta
Reading:
GMM: Kronecker Delta
W1 D2
Introduction to Fourier Series
Add Two Functions Fourier Making Waves
Guess the Fourier Series from a Graph
Reading After Class:
Fourier: Making Waves PhET
GMM: Fourier Exploration
HW 1a (w/ Solution)
HW 1a (pdf)
Computing Fourier Series
Fourier Approximation of a Step
Reading:
GMM: Fourier Coefficients
GMM: Fourier Example
GMM: Fourier Worked Example
Alternate Reading:
Taylor 5.7
Georgi 6.2
W1 D3
Abstract Vector Spaces
Properties of Abstract Vector Spaces
Reading:
GMM: Definition of a Vector Space
Abstract Inner Products
Visualizing the Dot Product
Visualizing the Dot Product in Higher Dimensions
Inner Products are a Generalization of the Dot Product
Reading:
GMM: Definition and Properties of an Inner Product
Reading After Class:
GMM: The Dot Product
GMM: Visualizing the Dot Product
GMM: Visualizing the Dot Product in Higher Dimensions
GMM: Visualizing the Product of Two Functions
W1 D4
Review: Linear ODEs
Reading:
GMM: Definitions for ODEs
GMM: Definition of Linear
GMM: Theorems for Linear ODEs
Optional, Advanced Reading:
GMM: Linear Independence
Review: Linear, homogeneous ODEs with constant coefficients.
Solving a SHO as a Homogeneous Linear Ordinary Differential Equation
Reading:
GMM: The Method for Homogeneous Equations with Constant Coefficients Optional Video:
Linear, Homogeneous ODEs with Constant Coefficients
Inhomogeneous Linear ODE's
Reading:
GMM: The Method for Inhomogeneous Equations
Optional Video:
Linear, Inhomogeneous ODEs with Constant Coefficients
Alternate Reading:
Taylor 5.5
Georgi 2.2
W1 D5
“A” Form of Simple Harmonic Motion (SHM)
Reading:
Taylor 5.2
Georgi 1.1
Reading After Class:
GMM: Sums of Harmonic Functions
HW 1b (w/ Solution)
HW 1b (pdf)
Using Initial/Boundary Conditions to Determine Solutions
W2 D1
Plane Pendulum
Force from Potential Energy
Pendulum Potential
Ubiquity of the SHO Equation
SHM “B”, “C”, & “D” Forms
Relating A, B, C, \& D Form of Simple Harmonic Motion
Reading:
Taylor 5.2
Georgi 1.1
A, B, C & D Forms of SHM Recap

Taylor 5.2

Georgi 1.1, 1.4

W2 D2
Acting out an LC circuit
HW 2a (w/ Solution)
HW 2a (pdf)
LC Circuit
Comparing Energies between Mass/Spring and LC
LIPA Inductors Section 11.12
LIPA LC Circuit Section 11.13
Parameters Simple Harmonic Motion: Frequency, Period, Phase
More Relative Phases
Free Motion of an Oscillator: Mass-Spring
Mass/Spring PhET Exploration
Visualizing Parameters of Oscillations

Taylor 5.2

Taylor 4.2 & 4.3

Georgi 1.1, 1.6

Mass Spring PhET

Motion of a damped oscillator

Taylor 5.4

Georgi 2.1

W2 D3
Undriven LRC Circuit
Undriven LRC Simulation
Forced motion of a damped mass-spring system
Forced Mass-Spring Mathlet
Forced motion of a RLC circuit
W2 D4
LRC Circuit investigation
LRC Lab
W2 D5
Forced motion of a damped oscillator: Resonance

Taylor 5.6

Georgi 2.3

HW 2b (w/ Solution)
HW 2b (pdf)
Forced motion of a damped oscillator: Admittance
W3 D1
Peer review of results - writing a scientific story
LRC Lab: Preliminary Discussion

Ph424 Report Writing Guidelines

Example Paper: McGuyer 2021

W3 D2
Admittance and Impedance
HW 3a (w/ Solution)
HW 3a (pdf)
Q- Factor in a Resonant Circuit
W3 D3
LRC lab - discussion and review

Example Paper: McGuyer 2021

Ph424 Report Writing Guidelines

How to (Seriously) Read a Scientific Paper

Writing Good Negative Reviews

W3 D4
Driving an oscillator at several frequencies
Fourier: Making Waves PhET
W3 D5
Recap time/freq Fourier Series, C-form, real space/k-space Fourier Series
HW 3b (w/ Solution)
HW 3b (pdf)
New Row
W4 D1
Derivation of Waves on a String
W4 D2
Derive the Wave Eqn in Springs/Masses
LRC Lab Report (w/ Solution)
LRC Lab Report (pdf)
Compare the Spring and String Derivations
Intro to Waves: Non-dispersive wave equation, Separation of Variables, PDEs, Initial conditions;
Properties of Waves

Taylor 16.1-16.3

Georgi 8.1

Main 9.1

GMM: Separation of Variables

W4 D3
Describing waves, velocities, traveling waves (Non-dispersive wave equation)
Properties of Waves
W4 D4
superpositions and Fourier series;Example - string under tension
Dispersion Relation

Taylor 16.3

Waves on a String

W4 D5
Reflection and transmission coefficients

Taylor 16.3

Georgi 9.1

HW 4b (w/ Solution)
HW 4b (pdf)
W5 D1
superpositions and Fourier series;Example - string under tension
Taylor 16.3
W5 D2
Coax Cable Lab- data
Coax Wave Lab
HW 5a (w/ Solution)
HW 5a (pdf)
W5 D3
Impedance; Reflection of force waves
Main 9.2, 9.4, 9.5
W5 D4
Wave propagation & attenuation
Main 9.2, 9.4, 9.5
W5 D5
Review
HW 5b (w/ Solution)
HW 5b (pdf)
Final Exam: Monday after Week 5