The position of a ball, u(t), rolling on a bump is modelled using the ODE d²u du dt² = 3u-2=. dt (a) Rewrite the above as a two-variable system of ODEs in (u, v) where v = du/dt. (b) Classify the fixed point. (c) Sketch the phase portrait. Your solution should include a calculation of any relevant eigenvectors.
The position of a ball, u(t), rolling on a bump is modelled using the ODE d²u du dt² = 3u-2=. dt (a) Rewrite the above as a two-variable system of ODEs in (u, v) where v = du/dt. (b) Classify the fixed point. (c) Sketch the phase portrait. Your solution should include a calculation of any relevant eigenvectors.
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Transcribed Image Text:The position of a ball, u(t), rolling on a bump is modelled using the ODE
d²u
du
dt²
= 3u - 2
dt
(a) Rewrite the above as a two-variable system of ODEs in (u, v) where v =
(b) Classify the fixed point.
= du/dt.
(c) Sketch the phase portrait. Your solution should include a calculation of any
relevant eigenvectors.
(d) Give the ggeneral inequality relating u(0) and v(0) for which the position of
the ball u →→∞ as t→→∞.
Note: It is not required that you solve the system.
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