     Calculus Animations,Graphics and Lecture Notes 2d order Diff EQS-Motion    Home About Kelly Liakos Sponsors Calculus 1- Limits and Derivatives Calculus 1 - The Second Derivative Calculus 1 and 3 Formula Sheets Chain Rule Computer Lab Assignments Conic Sections Differential Equations Directional Derivatives/Gradient Double Integrals Equillibrium Solutions 1st order DEs 1st order Diff Eqs -Motion Flux Integrals and Surface Integrals Infinite Sequences Infinie Series Level Curves and Level Surfaces Line Integrals Optimization and Related Rates Optimization for Functions of 2 Variables Parametric Equations 2-space Parametric Equations 3-space Partial Derivatives Polar Coordinate System Polar Coordinates- Derivatives and Integrals PreCalculus Riemann Sums and the Fundamental Theorem of Calculus 2d order Diff EQS-Motion 2d Partial Derivatives Supplemental Exercises and Solutions Tangent Planes/ Differential for f(x,y) Trigonometry Trigonometry Applications Triple Integrals Unit Tangent Vectors/Unit Normal Vectors Vectors in General Vector Valued Functions Visualizing Limits of Functions of 2 Variables Work Links Special Topics Scratch Paper 2 Poems  The following download is my lecture notes on the second order homogeneous differential equation with constant coefficients Lecture Notes 2d order homogeneous DEs with constant coefficients The following downloads are my lecture notes and animations for an application of second order homogeneous differential equations to the motion of a mass on a spring Lecture Notes Applcication of 2d order eqns to a mass on a spring undamped underdamped overdamped critcally damped The following 2 animations show the relationship between circular motion and the motion of a mass on a spring-first in the undamped case and then the underdamped case undamped Underdamped The following 2 animations show the relationship between circular motion and the linearized pendulum - again the first undamped and the second underdamped undamped underdamped

Finally we consider the non-homogeneous 2d order eqn and applications of an RLC circuit which includes both continuous and discontinuous forcing functions.
You may want to review the Unit Step Function Notes on the Differential Equations
Page before examining the discontinuous case.

Lecture Notes RLC Circuit

DISCONTINUOUS

The Smart Bunny-A very short story by Kurt Vonnegut Jr.  