Poles on a Complex Plane and Dynamic Response

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19 Terms

1
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Exponential decay

real, negative

<p>real, negative</p>
2
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Damped Sinusoidal behavior

imaginary, negative

<p>imaginary, negative </p>
3
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damped sinusoidal (ringing)

imaginary, negative

<p>imaginary, negative</p>
4
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Sustained oscillations

pure imaginary

<p>pure imaginary </p>
5
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exponential growing sinusoidal behavior (unstable)

imaginary, positive

<p>imaginary, positive </p>
6
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unbounded exponential growth (unstable)

real, positive

<p>real, positive</p>
7
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Unbounded exponential growth (unstable)

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8
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Exponential growing sinusoidal behavior (unstable)

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9
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Sustained oscillations

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10
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Damped Sinusoidal behavior (ringing)

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11
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Damped Sinusoidal behavior

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12
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Exponential decay

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13
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When is a process unstable?

if a pole is on the right half of the plane

14
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<p>exponential decay </p>

exponential decay

exponential decay

<p>exponential decay </p>
15
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<p>damped sinusoidal behavior </p>

damped sinusoidal behavior

damped sinusoidal behavior

<p>damped sinusoidal behavior </p>
16
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<p>damped sinusoidal behavior (ringing)</p>

damped sinusoidal behavior (ringing)

damped sinusoidal behavior (ringing)

<p>damped sinusoidal behavior (ringing)</p>
17
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<p>sustained oscillations</p>

sustained oscillations

sustained oscillations

<p>sustained oscillations</p>
18
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<p>exponential growing sinusoidal behavior (unstable)</p>

exponential growing sinusoidal behavior (unstable)

exponential growing sinusoidal behavior (unstable)

<p>exponential growing sinusoidal behavior (unstable)</p>
19
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<p>unbounded exponential growth (unstable)</p>

unbounded exponential growth (unstable)

unbounded exponential growth (unstable)

<p>unbounded exponential growth (unstable)</p>