Question

86. How is the differential equation for a second order circuit solved? 87. What is the characteristic equation of a second order circuit? 88. What is the importance of the roots of the characteristic equation of a second order circuit? 89. What are the components of the roots of the characteristic equation? Which meaning do they have? 90. Which major groups of final solutions are obtained depending on the structure of the roots of the characteristic equation?

Answer 1

86 Second order differential equation can be solved by . differential solution approach · Laplace transform approach 01) Characteristic equation is the Laplace transform of and order differenbial Equation. The sduhon of and order Equatwy depends on the location to snoola ob characteristic Equa- tion. .: System Response depends on noola roots have real part and imaginary parts, Let at bj The magnitude of systems response depends on the real part of the root The oscillation of response depends on the complex component of roos negitive Real part estable positive Real part → unstable.

case @ T ube If noots are real and unequal -a, -92 rool hipnot , sol= qe ait t. Cae-antonio case v dagat astro bre o 10 roots are read and equal, roots - -a stainstoon sol = (citet) eat wit case Id roots are complex Conjugate betroolis -atib sol= cophttCq Sinbt) e a