The motion of a mass on a spring is described by the equation mx" (t) + D x(t) = 0 where x(t) is the displacement at time t, m> 0 is the mass, D>0 is the spring constant and the parameters are given in Sl units. Let m = 0.25 and D = 1. a) What are the roots of the characteristic equation? b) What are the linearly independent solutions? c) What is the general solution x(t)? d) Find the solution if x(0) = 3 and x' (0) = 8.
The motion of a mass on a spring is described by the equation mx" (t) + D x(t) = 0 where x(t) is the displacement at time t, m> 0 is the mass, D>0 is the spring constant and the parameters are given in Sl units. Let m = 0.25 and D = 1. a) What are the roots of the characteristic equation? b) What are the linearly independent solutions? c) What is the general solution x(t)? d) Find the solution if x(0) = 3 and x' (0) = 8.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:The motion of a mass on a spring is described by the equation m x" (t) + D x(t) = 0 where x(t) is the
displacement at time t, m>0 is the mass, D>0 is the spring constant and the parameters are given
in Sl units. Let m = 0.25 and D= 1.
a) What are the roots of the characteristic equation?
b) What are the linearly independent solutions?
c) What is the general solution x(t)?
d) Find the solution if x(0) = 3 and x' (0) = 8.
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