Explore BrainMass

Explore BrainMass

    Evaluation the radius of curvature

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Curvature (III)
    Differential Calculus

    Evaluate the radius of curvature at any point (x,y) for the curves :

    (a) xy = c2 (b) y = (1/2)a(ex/a + e-x/a)

    See attached file for full problem description.

    © BrainMass Inc. brainmass.com March 4, 2021, 6:01 pm ad1c9bdddf
    https://brainmass.com/math/derivatives/evaluation-radius-curvature-23921

    Attachments

    Solution Preview

    Please see the attached file.

    Curvature (III)
    Differential Calculus

    Written by :- Thokchom Sarojkumar Sinha

    Evaluate the radius of curvature at any point (x,y) for the curves :
    (a) xy = c2 (b) y = (1/2)a(ex/a + e-x/a)

    Solution :- (a) xy = c2
    Differentiating the equation with respect to 'x' , we get
    y + x dy/dx = 0 --------------------------------------(1)
    or, y + xy1 = 0 where y1 = dy/dx
    or, xy1 = - y or, y1 = - y/x ------------------------------(1a)

    Again differentiating (1) with respect to 'x' , we get
    dy/dx + 1.dy/dx + x d2y/dx2 = 0
    or, 2dy/dx + xd2y/dx2 = 0 or, 2y1 + xy2 = 0 where y1 = dy/dx , y2 = d2y/dx2
    or, 2.(-y/x) + xy2 = 0 by using the relation y1 = - y/x
    or, - 2y/x + xy2 = 0 or, xy2 = 2y/x
    or, y2 = 2y/x2 ...

    Solution Summary

    This solution is comprised of a detailed explanation for finding the radius of curvature at any point of the curves.
    It contains step-by-step explanation for finding the radius of curvature at any point (x,y) for the curves :

    (a) xy = c2 (b) y = (1/2)a(ex/a + e-x/a)

    Solution contains detailed step-by-step explanation.

    $2.49

    ADVERTISEMENT