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3-040-FirstPassageTime-ModelingScenario

Author(s): Brian Winkel

SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations

Keywords: oscillator damped underdamped first passage first passage time spring mash dashpot

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Abstract

Resource Image We apply the notions of dampedness to second order, linear, constant coefficient, homogeneous differential equations used to model a spring mass dashpot system and introduce the notion of first passage time through 0 value with several applications.

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Differential Equation Type
Technique
Qualitative Analysis
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Description

In the differential equation of a spring mass system:

m y''(t) + c y'(t) +k y(t) = 0, say with y'(0) = 0, and y(0) = y0 > 0

for each of the values of k in this range of values find the time the mass first has a displacement of 0. For each value of k call this time the first passage time, FP(k).

All other things being equal, does initial position have anything to do with first passage? That is a question.

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Authors

Author(s): Brian Winkel

SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations

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