s11_mthsc208_hw09 - MthSc 208 Spring 2011(Differential...

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Unformatted text preview: MthSc 208, Spring 2011 (Differential Equations) Dr. Matthew Macauley HW 9 Due Monday February 28th, 2011 (1) A 0 . 1-kg mass is attached to a spring having a spring constant 3 . 6 kg/s 2 . The system is allowed to come to rest. Then the mass is given a sharp tap, imparting an instantaneous downward velocity of 0 . 4 m/s . If there is no damping present, find the amplitude A , frequency ω , and phase-shift φ , of the resulting motion. (a) Let x = 0 be the position of the spring before the mass was hung from it. Find x (0). (b) Solve this initial value problem and plot the solution. (2) A spring-mass system is modeled by the equation x 00 + μx + 4 x = 0 . (a) Show that the system is critically damped when μ = 4 kg/s . (b) Suppose that the mass is displaced upward 2 m and given an initial velocity of 1 m/s . Use a computer (i.e., WolframAlpha) to comute the solution for μ = 4, 4.2, 4.4, 4.6, 4.8, 5. Plot all of the solution curves on one figure. What is special about the critically damped solution in comparison to the other solutions?damped solution in comparison to the other solutions?...
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