Differences

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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.