Initial Condition - Partial Differential Equations - Solved Exam, Exams of Differential Equations

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MATH 348 - April 14, 2008 NAME: Ke Exam II - 50 Points - 50 minutes SECTION: Ce In order to receive full credit, SHOW ALL YOUR WORK. Full credit will be given only if all reasoning and work is provided. When applicable. please enclose your final answers in boxes. 1. (10 Points) Conceptual Questions. Suppose that we have the graph of the initial condition u(z,0) = f(a): (a) Assume that f is the initial temperature for a homogenous heat problem with boundary conditions, uz(0,t) = 0, uz(1,t) = 0. Describe the physical meaning of these boundary conditions and graph the approximate temperature profile for t — oc. v Malou’) = wlit)= © A . SSvumi 3 Implies no + + Cd ") Da no Eud points 4 \o . ay , of Woe ols eer — eines ewe Nanela ix Pew Are insulered frown Se ee CAureise. AGS ve would Weak bath ) We Abore or below Axis, (b) Assume that f is the initial displacement of an clastic string modeled by the homogenous wave equation subject to boundary conditions u(0, 4) = 0, u(1,t) = 0. Describe the physical caning of these boundary conditions and describe time-dynamics of the points, P; and 22, on this clastic string assuming that the string has no initial velocity. ~ Vikesee oe eee Wet Dan a Ws Coed O+ Bot, End ows. ?P \ usill @escillate Ybebusc]een } \) \4 taking on OM poms in lethwreer. Py, usi ll ey ae ie at time,