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The result is discussed under three different conditions as following: (1)underdamping wheniscalled underdamping,the solution is Uc=E-Ee-R cos+ (15) WhereEq.15 is called damping oscillation solution. (2)overdamping when0,it is called overdamping. The solution is Ue=E-号ele+水--7k 2r (16) Where,there is no oscillation in this case. (3)critical damping when0 it iscalled critical damping,the solution is U=E-E(1+Bte- (17) When the circuit achieves steady state,dropping the power supply suddenly(E-0),the changes periodic damping U square wave critical damping Fig8 Charge&discharge wave pattern of series RLC circuit5 The result is discussed under three different conditions as following: (1)underdamping when 0 2 0 2 β −ω < ,it is called underdamping,the solution is ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = − + − U E Ee t t t C ω ω β ω β cos sin (15) Where 2 2 ω = ω0 − β ,Eq. 15 is called damping oscillation solution. (2)overdamping when 0 2 0 2 β −ω > ,it is called overdamping. The solution is [( )( ) ]t t t C e e e r E U E 2 γ β γ β γ β γ − − = − + − − (16) Where 2 0 2 γ = β −ω , there is no oscillation in this case. (3)critical damping when 0 2 0 2 β −ω = ,it is called critical damping,the solution is ( ) t C U E E t e β β − = − 1+ (17) When the circuit achieves steady state, dropping the power supply suddenly (E=0), the changes Fig8 Charge& discharge wave pattern of series RLC circuit
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