1. The problem statement, all variables and given/known data Calculate RLC circuit responses to a step input? I believe the step input needs to be 10V. 2. Relevant equations Series RLC Characteristic Equation: S2 + S(R/L) + 1/LC = 0 Putting the above equation into standard form: S2 + 2αS + ω02 = 0, it follows that: α = R/2L ω0 = 1 / √LC where: α is the Damping Coefficient and ω0 is the Natural or Resonant Frequency The roots of the Characteristic Equation, by using the Quadratic Formula, are: S1,2 = -α ± √(α2 - ω02) For each type of damping condition, the voltage and current solutions take a different form: CAPACITOR VOLTAGE FOR A STEP INPUT TO A SERIES RLC CIRCUIT: Overdamped: α> ω0, Vc(t) = Vc(∞) + A1e S1t + A2e S2t Volts Critically Damped: α= ω0, Vc(t) = Vc(∞) + (A1 + A2t)e -αt Volts Underdamped: α< ω0, Vc(t) = Vc(∞) + (A1cos ωdt + A2 sin ωdt)e -αt Volts ωd = √(α2 - ω02) INDUCTOR CURRENT FOR A STEP INPUT TO A SERIES RLC CIRCUIT: Overdamped: α> ω0, IL(t) = IL (∞) + B1e S1t + B2e S2t Amps Critically Damped: α= ω0, IL (t) = IL (∞) + (B1 + B2t)e -αt Amps Underdamped: α< ω0, IL (t) = IL (∞) + (B1cos ωdt + B2 sin ωdt)e -αt Amps ωd = √(α2 - ω02) Can you please let me know if these formulas are correct to continue answering this question?