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--- notes:elen30009 [2021/05/24 01:47] – created joeleg
+++ notes:elen30009 [2023/05/30 22:32] (current) – external edit 127.0.0.1
@@ Line 178: / Line 178: @@
 ==== Types of natural response for parallel ====
-  *  $\omega_0^2<\alpha^2$
+  * ** $\omega_0^2<\alpha^2$ :**  $s_1$  and  $s_2$  are real and distinct,  $v(t)$  is over-damped (no oscillation).
- $s_1$  and  $s_2$  are real and distinct,  $v(t)$  is over-damped (no oscillation).
+  * ** $\omega_0^2=\alpha^2$ :**  $s_1$  and  $s_2$  are real and equal,  $v(t)$  is critically damped (verge of oscillation).
-  *  $\omega_0^2=\alpha^2$
+  * ** $\omega_0^2>\alpha^2$ :**  $s_1$  and  $s_2$  are complex,  $v(t)$  is under-damped (voltage oscillates about final value with oscillation frequency  $\omega_d=\sqrt{\omega_0^2-\alpha^2}$ ).
- $s_1$  and  $s_2$  are real and equal,  $v(t)$  is critically damped (verge of oscillation).
-  *  $\omega_0^2>\alpha^2$
- $s_1$  and  $s_2$  are complex,  $v(t)$  is under-damped (voltage oscillates about final value with oscillation frequency  $\omega_d=\sqrt{\omega_0^2-\alpha^2}$ ).
 All of the following can be done in terms of current with minimal changes.