Free Mechanical Vibrations Section 3.7 Free Mechanical Vibrations: Problem 5 (1

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Free Mechanical Vibrations

Section 3.7 Free Mechanical Vibrations: Problem 5 (1 pt) This problem is an example of over-damped harmonic motion. A mass m = 4 is attached to both a spring with spring constant k = 288 and a dash-pot with damping constant c = 68. The ball is started in motion with initial position x0 = -9 and initial velocity v0 = 5 . Determine the position function x(t). x(t) = Graph the function x(t). Now assume the mass is set in motion with the same initial position and velocity, but with the dashpot disconnected ( so c = 0). Solve the resulting differential equation to find the position function u(t). In this case the position function u(t) can be written as u(t) = C0cos(w0t - a0). Determine C0, w0 and a0. Finally, graph both function x(t) and u(t) in the same window to illustrate the effect of damping.

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