# if you fell into a tube through the earth

**URL:** <https://boards.straightdope.com/t/if-you-fell-into-a-tube-through-the-earth/158261>\
**Category:** Cecil's Columns/Staff Reports\
**Created:** [February 28, 2003, 11:11pm UTC](https://boards.straightdope.com/t/if-you-fell-into-a-tube-through-the-earth/158261 "2003-02-28T23:11:55Z")\
**Posts on this page:** 2\
**Page:** 3

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**Author:** ![The\_Ryan](https://avatars.discourse-cdn.com/v4/letter/t/7feea3/32.png) [@The\_Ryan](https://boards.straightdope.com/u/The_Ryan)\
**Post date:** [March 17, 2003, 12:26am UTC](https://boards.straightdope.com/t/if-you-fell-into-a-tube-through-the-earth/158261/41 "2003-03-17T00:26:29Z")

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After thinking it about it a bit more, I see now that my previous statement can be interpreted in such a way that it is incorrect. So let me amend it to this: there is no nontrivial solution to the CDHO case with an initial zero veloctiy in which an intersection with the equilibrium point lies in the future. I there a conter example I missed?

PS While most solutions to the CDHO cross once, the purely exponential solution won’t cross at all.

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**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\
**Post date:** [March 17, 2003, 10:07pm UTC](https://boards.straightdope.com/t/if-you-fell-into-a-tube-through-the-earth/158261/42 "2003-03-17T22:07:58Z")

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D’oh! I was forgetting the zero initial velocity part. And there are certainly at least some cases of zero initial velocity, critically damped, where you never cross the axis: Take the one-crossing solution, and set t=0 at the turnaround point on the far side.

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