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) = 9-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) + (9 − 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. x(t) = ☐ +... (Type an expression that includes all terms up to order 4.) k(t)=9-t mrr 1 N-sec/m 2 kg heat x(t) x(0)=2 x'(0)=0

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) = 9-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) + (9 − 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. x(t) = ☐ +... (Type an expression that includes all terms up to order 4.) k(t)=9-t mrr 1 N-sec/m 2 kg heat x(t) x(0)=2 x'(0)=0

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.7: Applications

Problem 18EQ

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