A certain springmass system satisfies the initial value
Chapter 6, Problem 16(choose chapter or problem)
A certain springmass system satisfies the initial value problemu+ 14u+ u = kg(t), u(0) = 0, u(0) = 0,where g(t) = u3/2(t) u5/2(t) and k > 0 is a parameter.(a) Sketch the graph of g(t). Observe that it is a pulse of unit magnitude extending overone time unit.(b) Solve the initial value problem.(c) Plot the solution for k = 1/2, k = 1, and k = 2. Describe the principal features of thesolution and how they depend on k.(d) Find, to two decimal places, the smallest value of k for which the solution u(t) reachesthe value 2.(e) Suppose k = 2. Find the time after which |u(t)| < 0.1 for all t >
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