- #1

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i don't know slove the equation

[tex]x"=k/m*x[/tex] (1)

i don't understand result of (1) is [tex]x=Asinkt+Bcoskt[/tex]

- Thread starter tuananh3ap
- Start date

- #1

- 18

- 0

i don't know slove the equation

[tex]x"=k/m*x[/tex] (1)

i don't understand result of (1) is [tex]x=Asinkt+Bcoskt[/tex]

- #2

CompuChip

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- #3

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who can help me. thank you very much

- #4

CompuChip

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If you know about complex numbers, there is a more elegant way (which also works for more general equations). That is to plug in a trial solution [itex]x = e^{\lambda t}[/itex]. Then the differential equation will give you an equation for [itex]\lambda[/itex], whose roots provide the n independent solutions (for an n-th order differential equation, in this case, n = 2).

I can work out the example for you, but you better tell me whether you know about complex numbers and stuff like

[tex]e^{i\theta} = \cos\theta + i \sin\theta[/tex]

before I do a lot of work for nothing

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