Consider the following homogeneous linear DE: y" + 8a y' + 4 y(t) = 0 where a is a constant. Indicate for what intervals of a the system is undamped, under- damped, critically damped, and over-damped. In each case, (i) give a qualitative description of the oscillations, (ii) give an expression for the roots of the characteristic equation in terms of a – simplify as much as possible, and state if the roots are real, or imaginary (complex). iii) write the general solution for undamped, under-damped, critically damped, and over- damped (in terms of a if necessary).

Consider the following homogeneous linear DE: y" + 8a y' + 4 y(t) = 0 where a is a constant. Indicate for what intervals of a the system is undamped, under- damped, critically damped, and over-damped. In each case, (i) give a qualitative description of the oscillations, (ii) give an expression for the roots of the characteristic equation in terms of a – simplify as much as possible, and state if the roots are real, or imaginary (complex). iii) write the general solution for undamped, under-damped, critically damped, and over- damped (in terms of a if necessary).

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter11: Differential Equations

Section11.1: Solutions Of Elementary And Separable Differential Equations

Problem 54E: Plant Growth Researchers have found that the probability P that a plant will grow to radius R can be...

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