## x = Acos(ωt) + Bsin(ωt) derivation

How do you derive x = Acos(ωt) + Bsin(ωt) from F = -mω2x and what is the former used for?

Thank you!!
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 Recognitions: Homework Help Hey sparkle! If this is homework, you should show some effort before we're allowed to help you (PF regulations I'm afraid). What's it for?
 This was on a list of things you should know for physics contests. :)

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## x = Acos(ωt) + Bsin(ωt) derivation

Well, what can you make of it?
 Well, F = -mω2x is hooke's law and SHM for a spring is like x = Asin(ωt)
 Recognitions: Homework Help So what's your question? Actually, F=ma and "a" is the second derivative of "x" with respect to time. So you have mx''=-mω2x. The general solution to this differential equation is x = Acos(ωt) + Bsin(ωt).
 so would you get from Acos(ωt) + Bsin(ωt) to Asin(ωt)? thanks!

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Homework Help
 Quote by sparkle123 so would you get from Acos(ωt) + Bsin(ωt) to Asin(ωt)? thanks!
The relation is:
$$A\cos(ωt) + B\sin(ωt) = \sqrt{A^2+B^2}\sin(ωt+θ_0)$$
 thank you! :)