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As a spring is heated, its spring “constant” decreases in value. Suppose a spring is heated...

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Advance Math

As a spring is heated, its spring “constant” decreases in value.Suppose a spring is heated so that the spring “constant” at time tis k(t) = 6 ? t. If the unforced mass-spring system has mass m = 2kg and a damping constant b = 1 N-sec/m with initial conditionsx(0) = 3 m and x' (0) = 0 m/sec, then the displacement x(t) isgoverned by the initial value problem 2x'' + x' ? (6 ? t)x = 0;x(0) = 3, x' (0) = 0.

Find the first four nonzero terms in a power series solutioncentered at t = 0.

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