As a spring is heated, its spring "constant" decreases. Suppose the spring is heated so that the spring "constant" at time t is k(t) = 5 –t N/m. If the unforced mass-spring system has mass m =2 kg and a damping constant b = 1 N-sec/m with initial conditions x(0) = 2 m and x'(0) = 0 m/sec, then the displacement x(t) is governed by the initial value problem 2x"(t) + x'(t) + (5 – t)x(t) = 0; x(0) = 2, x'(0) = 0. Find the first four nonzero terms in a power series expansion about t= 0 for the displacement. k(t)=5-t 1 N-sec/m lellll 2 kg heat x(t) x(0)=2 x'(0)=0 x(t) = +... (Type an expression that includes all terms up to order 4.)
As a spring is heated, its spring "constant" decreases. Suppose the spring is heated so that the spring "constant" at time t is k(t) = 5 –t N/m. If the unforced mass-spring system has mass m =2 kg and a damping constant b = 1 N-sec/m with initial conditions x(0) = 2 m and x'(0) = 0 m/sec, then the displacement x(t) is governed by the initial value problem 2x"(t) + x'(t) + (5 – t)x(t) = 0; x(0) = 2, x'(0) = 0. Find the first four nonzero terms in a power series expansion about t= 0 for the displacement. k(t)=5-t 1 N-sec/m lellll 2 kg heat x(t) x(0)=2 x'(0)=0 x(t) = +... (Type an expression that includes all terms up to order 4.)
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:As a spring is heated, its spring "constant" decreases. Suppose the spring is
heated so that the spring "constant" at timet is k(t) = 5 -t N/m. If the unforced
mass-spring system has mass m=2 kg and a damping constant b = 1
N-sec/m with initial conditions x(0) = 2 m and x'(0) = 0 m/sec, then the
displacement x(t) is governed by the initial value problem
2x''(t) + x'(t) + (5 – t)x(t) = 0; x(0) = 2, x'(0) = 0. Find the first four nonzero terms
in a power series expansion about t=0 for the displacement.
k(t)=5-t
1 N-sec/m
2 kg
heat
x(t)
x(0)=2
%3D
x'(0)=0
x(t) =
+...
(Type an expression that includes all terms up to order 4.)
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