The remaining problems in this section deal with free damped motion. In Problems 15 through 21, a

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The remaining problems in this section deal with free damped motion. In Problems 15 through 21, a mass m is attached to both a spring (with given spring constant k) and a dashpot (with given damping constant c). The mass is set in motion with initial position x0 and initial velocity v0. Find the position function x(t) and determine whether the motion is overdamped, critically damped, or underdamped. If it is underdamped, write the position function in the form x(t) = C1e-pt cos(ω1t - α1). Also, find the undamped position function u(t) = C0 cos(ω0t - α0) that would result if the mass on the spring were set in motion with the same initial position and velocity, but with the dashpot disconnected (so c = 0). Finally, construct a figure that illustrates the effect of damping by comparing the graphs of x(t) and u(t).

m = 2 , c = 12, k = 50 ; x0 = 0, v0 = -8

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Differential Equations And Linear Algebra

ISBN: 9780134497181

4th Edition

Authors: C. Edwards, David Penney, David Calvis

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