Given a mass m, a dashpot constant c, and a spring constant k, Theorem 2 of Section
Question:
Given a mass m, a dashpot constant c, and a spring constant k, Theorem 2 of Section 5.1 implies that the equation
has a unique solution for t ≧ 0 satisfying given initial conditions x (0) = x0, x'(0) = v0. Thus the future motion of an ideal mass-spring-dashpot system is completely determined by the differential equation and the initial conditions. Of course in a real physical system it is impossible to measure the parameters m, c, and k precisely. Problems 35 through 38 explore the resulting uncertainty in predicting the future behavior of a physical system.
Suppose that m = 1 and c = 2 but k = 1-10-2n. Show that the solution of Eq. (26) with x (0) = 0 and x'(0) = 1 is
mx" + cx' + kx = 0 (26)
Step by Step Answer:
The characteristic equation r 2r 110 0 has roots r110 Whe...View the full answer
Differential Equations And Linear Algebra
ISBN: 9780134497181
4th Edition
Authors: C. Edwards, David Penney, David Calvis
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