Geometry of Solutions

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Last updated 5:37 AM on 6/25/26
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10 Terms

1
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if the solution is a ± ib form…

the Solution is spiraling.

2
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if the solution is ±ib form

then it is NOT spiraling. It’s a closed ellipse or circle

3
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The solution is a perfect circle if?

The sin/cos all have the same amplitude

4
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Counterclockwise if?

-sin(t) is on top

5
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Clockwise if?

-sin(t) is on bottom

6
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If the a is positive its…

spiraling outward, increasing exponentially

7
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if there is a negative a…

spiraling inward

8
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If root one and two are both real, distinct, and opposite sign?

Saddle Point

9
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If both roots are real and positive?

Unstable Node

10
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If both roots are real, distinct, and negative?

Stable Node