# Question 21. The electric circuit shown in Figure 7.6.7 is described by the system of differential equations (33) (4)-(41)() where I is the current through the inductor and Vis the voltage drop across the capacitor. These differential equations were derived in Problem 16 of Section 7.1 a. Show that the eigenvalues of the coefficient matrix are real and different if L > 4R2C; show that they are complex conjugates if L < 4R2C. b. Suppose that R=112, C = 3, and L = 1 H. Find the general solution of the system (33) in this case. с R w L

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Transcribed Image Text: 21. The electric circuit shown in Figure 7.6.7 is described by the system of differential equations (33) (4)-(41)() where I is the current through the inductor and Vis the voltage drop across the capacitor. These differential equations were derived in Problem 16 of Section 7.1 a. Show that the eigenvalues of the coefficient matrix are real and different if L > 4R2C; show that they are complex conjugates if L < 4R2C. b. Suppose that R=112, C = 3, and L = 1 H. Find the general solution of the system (33) in this case. с R w L
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Transcribed Image Text: 21. The electric circuit shown in Figure 7.6.7 is described by the system of differential equations (33) (4)-(41)() where I is the current through the inductor and Vis the voltage drop across the capacitor. These differential equations were derived in Problem 16 of Section 7.1 a. Show that the eigenvalues of the coefficient matrix are real and different if L > 4R2C; show that they are complex conjugates if L < 4R2C. b. Suppose that R=112, C = 3, and L = 1 H. Find the general solution of the system (33) in this case. с R w L