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R L (3)1 The electric circuit shown above is described by the system of differential equations: 0 d dt V RC where I is the current through the inductance and V is the voltage drop across the capacitor. The system can be derived using Kirchoff's Laws and definitions of resistance (R), inductance (L), and capacitance (C). We will take it as a given! (a) Show that the eigenvalues of the coefficient matrix are real and distinct if L> 4R2C and that they are complex and conjugate if L< 4R2C.

R L (3)1 The electric circuit shown above is described by the system of differential equations: 0 d dt V RC where I is the current through the inductance and V is the voltage drop across the capacitor. The system can be derived using Kirchoff's Laws and definitions of resistance (R), inductance (L), and capacitance (C). We will take it as a given! (a) Show that the eigenvalues of the coefficient matrix are real and distinct if L> 4R2C and that they are complex and conjugate if L< 4R2C.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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R L (3)1 The electric circuit shown above is described by the system of differential equations: 0 d dt V RC where I is the current through the inductance and V is the voltage drop across the capacitor. The system can be derived using Kirchoff's Laws and definitions of resistance (R), inductance (L), and capacitance (C). We will take it as a given! (a) Show that the eigenvalues of the coefficient matrix are real and distinct if L> 4R2C and that they are complex and conjugate if L< 4R2C.
Transcribed Image Text:R L (3)1 The electric circuit shown above is described by the system of differential equations: 0 d dt V RC where I is the current through the inductance and V is the voltage drop across the capacitor. The system can be derived using Kirchoff's Laws and definitions of resistance (R), inductance (L), and capacitance (C). We will take it as a given! (a) Show that the eigenvalues of the coefficient matrix are real and distinct if L> 4R2C and that they are complex and conjugate if L< 4R2C.
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