The equation of motion of a springmass system with damping (see Section 3.7) is md2u dt2
Chapter 9, Problem 17(choose chapter or problem)
The equation of motion of a springmass system with damping (see Section 3.7) is md2u dt2 + c du dt + ku = 0, where m, c, and k are positive. Write this second order equation as a system of two first order equations for x = u, y = du/dt. Show that x = 0, y = 0 is a critical point, and analyze the nature and stability of the critical point as a function of the parameters m, c, and k. A similar analysis can be applied to the electric circuit equation (see Section 3.7) L d2I dt2 + R dI dt + 1 C I = 0.
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