Consider 2 + 8x + 16x = 0, with x(0) = 2 and (0) = 0....

   

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Consider 2ï + 8x + 16x = 0, with x(0) = 2 and (0) = 0. (a) Determine the values of X1,2. (b) State the class of motion (over, under, or critically damped). (c) For the given initial conditions, determine the most convenient form of the solution from those given in Window 1.5 (p. 25) of the text and write it out using the appropriate numerical values for all terms. (d) Sketch the solution but make sure your sketch properly represents the basic form of the solution, for example: the i.c.'s, the period Ta, and the number of cycles needed for the motion to cease (using Q ~ 1/2(). (e) Sketch the exponential decay envelope with dashed lines. Consider 2ï + 8x + 16x = 0, with x(0) = 2 and (0) = 0. (a) Determine the values of X1,2. (b) State the class of motion (over, under, or critically damped). (c) For the given initial conditions, determine the most convenient form of the solution from those given in Window 1.5 (p. 25) of the text and write it out using the appropriate numerical values for all terms. (d) Sketch the solution but make sure your sketch properly represents the basic form of the solution, for example: the i.c.'s, the period Ta, and the number of cycles needed for the motion to cease (using Q ~ 1/2(). (e) Sketch the exponential decay envelope with dashed lines.