Lab_14_2011 - GG303 Lab 14 11/23/11 1 FOLDS Exercise 1:...

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GG303 Lab 14 11/23/11 1 14-1 FOLDS Exercise 1: Graphical solution for curvature (10 points total) Find the curvature graphically at the crest of the curve on the next page using the three marked points and the procedure described in the notes for the lab lecture. A Give the absolute value of the curvature in cm -1 to 2 significant figures. 4 pts for graphical construction, 2 points for curvature value (2 points if within 0.2 cm -1 , 1 point if within 0.5 cm -1 , 0 pts if answer is off by more than 0.5 cm -1 ). B Explain whether your solution is greater than or is less than the true curvature value at the crest. (2 pts) C Explain whether you think you would get a more accurate graphical solution if the points were more closely spaced. Give a practical answer, not just a theoretical answer. (2 pts)
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GG303 Lab 14 11/23/11 2 14-2
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GG303 Lab 14 11/23/11 3 14-3 Exercise 2: Analytical solution for curvature (40 points total) Calculate the curvature of the following curves using the formula most college-level calculus books derive for the curvature of a plane curve: k = |y”|/[(1+{y’} 2 ) 3/2 ]: a y = x 1/3 (an inverse cubic function); b y = sin(x) (sine wave); c y = atan(x) (arctangent, a function resembling a monocline); d y = x 4 - 2x 2 + 1 (function that yields the shape of a beam with a constant overpressure on one side, the shape is like that of a laccolith); A Derive the solutions for the first derivative of y with respect to x (i.e., y’)
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Lab_14_2011 - GG303 Lab 14 11/23/11 1 FOLDS Exercise 1:...

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