Consider a battery of constant voltage E₀ that charges the capacitor shown in Figure 7.3.9. Divide equation (20) by L and define 2λ = R/L and ω² = 1/LC.

Use the Laplace transform to show that the solution q(t) of q'' + 2λq' + ω²q = E₀/L subject to q(0) = 0, i(0) = 0 is

Transcribed Image Text:

- e " (cosh VA – wt sinh VA – w?t) VA - w q(t) = { E,C[1 - e (1 + At)], A = w, E,C1- e"(cos Vo – x?t A< w. sin Vo - X1). Vo -