(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 Iuml and A in Eq (30 28) are given by Fig 30 17 tan o and A 2LV(1 LC) (R 4L) 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

Question: (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

(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

tan o and A = 2LV(1/LC) – (R²/4L²) cos o

Fig 30.17

When switch S is in this position, the emf charges the capacitor. +q el When switch S is moved to this position, the cap

tan o and A = 2LV(1/LC) (R/4L) cos o When switch S

tan o and A = 2LV(1/LC) (R/4L) 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.

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