530_343lecture07

# 530_343lecture07 - ME 530.343 Design and Analysis of...

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Spring 2009 Lecture 7 2 nd -Order Linear, Homogeneous, Time-Invariant ODE’s Monday, February 16, 2009 Today’s Objectives Purpose of today’s lecture: Solution(s) to uncoupled, linear, homogeneous, constant-coeﬃcient, 2 st order, ordinary diﬀer- ential equations. Important variables ζ , ω n , ω d , and the poles Reading: Chapter 5 1 First Order ODEs Very straightforward. See example and solution from previous lecture. 2 Second Order ODEs 2.1 Motivating example: Bungee jumping bungee jumper, mass m bungee cord of natural length L n air resists w/ damping constant b when the bungee cord is stretched spring k distance between the bungee jumper and the system’s equilibrium position, y Equation of motion is of the form: m ¨ y + b ˙ y + ky = 0 Questions: Will I die because I hit the river that is 100 m below the bridge? Will I die because the bungee cord breaks (max tensile strength is 5000 N)? Will I die because I bounce back too high and the cord goes slack and wraps around my neck? 1

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530_343lecture07 - ME 530.343 Design and Analysis of...

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