this post was submitted on 15 Jan 2025

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Daily Maths Challenges

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[2025/01/15] Twice derivative of function (lemmy.world)

submitted 3 weeks ago by siriusmart to c/dailymaths

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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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[–] siriusmart 2 points 3 weeks ago* (last edited 3 weeks ago)

This challenge requires some specific knowledge on the topics, so if you have no idea how to approach this question, take a hint

Initial hint

Maclaurin series: https://openstax.org/books/calculus-volume-2/pages/6-introduction

If you found f but not in the specific format

hint

R formula: https://brilliant.org/wiki/trigonometric-r-method/

No hints on the extension, you are on your own.