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

submitted 1 month 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] 2 points 1 month ago* (last edited 1 month ago)

That's why one usually searches for non trivial solution of differential equations. The trivial solution f(x)=0, in physics: "nothing happens", is usually not of interest, as we know by experience that something must happen to a system when some initial action is performed, yet mathematically it is always there.