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For the circuit of Figure 1.1: 50kQ 1 μF WWE 200 k2 1 με Figure 1.1 a. Derive the transfer function relating the input voltage v₁ and output voltage vo b. Determine function vo(t) when a 4V step input is applied. c. Using the initial and final value theorem, find the initial and final value of the output voltage when the input in part b above is applied? ii. For the following function, determine if pole-zero cancellation can be approximated. F(s) = (s + 3) (s +2.5) (s+4)² iii. Consider the following differential equation: d² x dx +5 + 8x = f(x) dt² dt where f(x) is the input and a function of the output x. If f(x) = e, linearize the differential equation for x hear 0. (Total 5+5+5+5+5=25 marks) W v (1)