(a) Take first and second derivatives with respect to time of q given in Eq. (30.28), and show that it is a solution of Eq (30.27).

(b) At t = 0 the switch shown in Fig. 30.17 is thrown so that it connects points d and a; at this time, q = Q and i = dq/dt = 0. Show that the constants Ï• and A in Eq. (30.28) are given by

Fig 30.17

Transcribed Image Text:

tan o and A = 2LV(1/LC) – (R²/4L²) cos o When switch S is in this position, the emf charges the capacitor. +q el When switch S is moved to this position, the capacitor discharges through the resistor and inductor.