How can I write the following equation as a first-order vector differential equation? <mtable c

hughy46u 2022-05-29 Answered
How can I write the following equation as a first-order vector differential equation?
m d 2 x d 2 t + 2 γ m d x d t + k x = 0 .
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Answers (1)

1c2ru3x
Answered 2022-05-30 Author has 9 answers
Introduce a new variable y ( t ) = x ˙ ( t ). Then
x ˙ ( t ) = y ( t ) y ˙ ( t ) = k m x ( t ) 2 γ y ( t )
Then if we take v = [ x y ] and A = [ 0 1 k m 2 γ ] , we have the following vector differential equation:
d d t v ( t ) = A v ( t ) .

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