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a) Draw the phasor circuit for the network given in Figur. Prove that the forced response is given by if (t) = 2.4 cos(3t+53.1°). The 2nd order differential equation describing the total current response i(t) is found as d²2-2+ i = -24 sin 3t. Find the characteristics equation and derive the natural response in (t). Hence, comment on the stability of the circuit. dt 122 Ww= IF -ODIDO 4 cos 3t V IH a. 2π W b) Suppose that a resister R carries a current i = Im cos wt with period T = What would be the instantaneous power dissipate across the above resister. Prove that the period of the instantaneous power Tp = /2 (Hint: instantaneous power dissipate across a resistor is p(t) = Ri(t)²). c) The behavior of an instantaneous power p(t) is described by Figure. Determine the average power P (Hint: Average power P = 1₁+pp(t)dt). Tp Jt₁ p(1) (W) JAA >1 (8) 3 -10