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ragman
 3 years ago
needed help with solving linear time invariant differential equations
ragman
 3 years ago
needed help with solving linear time invariant differential equations

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

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

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

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

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

UnkleRhaukus
 3 years ago
Best ResponseYou've already chosen the best response.0the characteristic equation ?

ragman
 3 years ago
Best ResponseYou've already chosen the best response.0so 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

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

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

ragman
 3 years ago
Best ResponseYou've already chosen the best response.0i knew i was forgetting something

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

ragman
 3 years ago
Best ResponseYou've already chosen the best response.0ok 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

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

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

UnkleRhaukus
 3 years ago
Best ResponseYou've already chosen the best response.0the 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 \[\mathcal L\{1\}(s)=\frac 1s\]
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