The remaining problems in this section deal with free
Chapter , Problem 15(choose chapter or problem)
The remaining problems in this section deal with free damped motion. In 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 / D C1ept cos.!1t 1/. Also, find the undamped position function u.t / D C0 cos.!0t 0/ 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 D 0). Finally, construct a figure that illustrates the effect of damping by comparing the graphs of x.t / and u.t /. 1
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