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)=7-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) = 4 m and x'(0) = 0 m/sec, then the displacement x(t) is governed by the initial value problem 2x'' (t) + x'(t)+(7-t)x(t) = 0; x(0) = 4, x'(0) = 0. Find the first four nonzero terms in a power series expansion about t=0 for the displacement.

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)=7-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) = 4 m and x'(0) = 0 m/sec, then the displacement x(t) is governed by the initial value problem 2x'' (t) + x'(t)+(7-t)x(t) = 0; x(0) = 4, x'(0) = 0. Find the first four nonzero terms in a power series expansion about t=0 for the displacement.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter11: Differential Equations

Section11.1: Solutions Of Elementary And Separable Differential Equations

Problem 59E: According to the solution in Exercise 58 of the differential equation for Newtons law of cooling,...

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