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ragman
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needed help with solving linear time invariant differential equations
 2 years ago
 2 years ago
ragman Group Title
needed help with solving linear time invariant differential equations
 2 years ago
 2 years ago

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ragman Group TitleBest ResponseYou've already chosen the best response.0
obtain the solution x(t) of the differential equation
 2 years ago

ragman Group TitleBest ResponseYou've already chosen the best response.0
dw:1347265100080:dw
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.0
\[\ddot x+\omega_n^2x=t\]
 2 years ago

ragman Group TitleBest ResponseYou've already chosen the best response.0
yup thats what i tried to write
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.0
\[m^2+\omega_n^2=0\]
 2 years ago

ragman Group TitleBest ResponseYou've already chosen the best response.0
would it be possible to explain that ?
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.0
the characteristic equation ?
 2 years ago

ragman Group TitleBest ResponseYou've already chosen the best response.0
so the first thing you would do is use the laplace transform on everything right im just not sure how to figure out how to do it for the w shaped variable
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.0
omega ? \(\omega_n^2\) is a constant for constant n
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.0
im not sure how you are going to use Laplace if you dont have any initial values
 2 years ago

ragman Group TitleBest ResponseYou've already chosen the best response.0
dw:1347266422040:dw
 2 years ago

ragman Group TitleBest ResponseYou've already chosen the best response.0
i knew i was forgetting something
 2 years ago

ragman Group TitleBest ResponseYou've already chosen the best response.0
and yeah i meant omega
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.0
well if we are going to use laplace transform you can forget the characteristic equation
 2 years ago

ragman Group TitleBest ResponseYou've already chosen the best response.0
ok sounds good the only difficulty i face is when things like omega come up i just get confused as to how im supposed to find the laplace transform of it
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.0
its just a positive constant, if you want to set \[\omega_n^2=A,\qquad A>0\]
 2 years ago

ragman Group TitleBest ResponseYou've already chosen the best response.0
ok im sorta getting it so what would the laplace transform of this constant be
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.0
the laplace transform of a constant times a function is the constant times the transfer \[\mathcal L\{αf(t)\} = α\mathcal L\{f(t)\}\] the laplace transform of one is one on the the transfer parameter \[\mathcal L\{1\}(s)=\frac 1s\]
 2 years ago
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