As a spring is heated, its spring "constant" decreases. Suppose the spring is heated so that the spring "constant" at ti

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As A Spring Is Heated Its Spring Constant Decreases Suppose The Spring Is Heated So That The Spring Constant At Ti 1 (21.85 KiB) Viewed 26 times

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. x(t)=₁ + ... (Type an expression that includes all terms up to order 4.) k(t) = 5-t m heat 2 kg 1 N-sec/m x(t) x(0) = 2 x'(0)=0