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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The last two questions in the second image is important which should be answered, the first image is about power series expansion scenario.
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