Q3 (a) Consider the first-order RC circuit as shown in Figure Q3.1. Determine the output voltage, vo(t) by using Laplace Transform. Given that v(t) = te³tu(t), R = 2 and C 0.5 F. (b) + 20 vo(t) v(t) = te ³tu(t) 0.5 F Figure Q3.1 Given a signal z(t) as shown in Figure Q3.2. z(t) (i) 1 2 3 Figure Q3.2 t Write the mathematical expression for z(t) in term of unit step and unit ramp. (ii) Find the Laplace transform for the z(t) using Laplace definition. (Hint: refer Laplace Transform Properties Table to solve Ste- -st dt) (iii) Proof your answer in Q3(b)(ii) using the mathematical expression in Q3(b)(i). (c) Determine an appropriate impulse response, h(t) for a stable system, if the system function, H(s) is given as: H(s) = S+3 (s-4)(s 3) 7 S-4 6 S-3 4