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[2025/01/15] Twice derivative of function (lemmynsfw.com)

submitted 3 months ago by [email protected] to c/[email protected]

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Question

Find the function f such that f'' = -f
Show that the function can be written in format f = A sin(x + B)

Extension

Find a function g such that g'' = C * -g and

g(0) = D
g'(0) = 0 where C and D are arbitrary constants.

For those who have finished the extension

Congratulations, you have just derived the formula for objects in simple harmonic motions (physics).

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[–] [email protected] 3 points 3 months ago* (last edited 3 months ago)

For simplicity, I restricted my solution to the 'extension' part and embedded the first part into it.
I hope it is OK to upload it here.
The task is a neat example to train the procedure of finding a solution to ODEs with initial value problems.

Thank you!

Solution.