Section 3.7 Free Mechanical Vibrations: Problem 4 (1 pt) This problem is an exam

Question

Section 3.7 Free Mechanical Vibrations: Problem 4 (1 pt) This problem is an example of critically damped harmonic motion. A mass m = 7 is attached to both a spring with spring constant k = 175 and a dash-pot with damping constant c = 70. The ball is started in motion with initial position x0 = 8 and initial velocity y0 = -44. Determine the position function 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.

Explanation / Answer

An ideal mass

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