Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §14.4 Cylindrical and Spherical Coordinates, #42 · Multivariable Calculus · Change of variables

Dig a tunnel through the center to Australia

Dig a tunnel through the center to Australia. Drop a ball in the tunnel at $y = R$ ; Australia is $y = - R$ . The force of gravity is $- cy$ by Problem 41. Newton's law is $m y^{''} = - cy$ . What does the ball do when it reaches Australia?

This exercise builds on another exercise in its source book, which isn't shown here.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §14.4 Cylindrical and Spherical Coordinates, #42

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