s11_mthsc208_hw09

s11_mthsc208_hw09 - MthSc 208, Spring 2011 (Differential...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 , and phase-shift , 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 + x + 4 x = 0 . (a) Show that the system is critically damped when = 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 = 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?...
View Full Document

Ask a homework question - tutors are online