Process Formula 2 - imaginary part y t approaches yp...

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Mass Balance on a Draining Tank: Drain Flow α Sq. root of Hydrostatic Head Linearization – Taylor Series: First Order ODE: Second Order ODE: Second Order Underdamped Form: Case 1: ξ > 1 (overdamped): [Stable] real negative distinct roots, − p 1, − p 2 y ( t ) approaches yp slowly, exponentially, without oscillations Case 2: ξ = 1 (critically damped): [Stable] real negative repeated roots y ( t ) approaches yp exponentially and without oscillations Case 3: 0 < ξ < 1 (underdamped): [Stable] distinct roots with a negative real part and an
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Unformatted text preview: imaginary part y ( t ) approaches yp exponentially and with oscillations Case 4: ξ = 0 (undamped): [Stable] repeated roots with an imaginary part and no real part Oscillations with constant amplitude , indicate a system at the limit of stability Case 5: ξ < 0 (unstable): [Unstable] All values of the damping factor, ξ, that are less than zero yield a solution that has a positive real part e + t will grow without bound and the process will display diverging...
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