Perform the following operation for the given block diagram:
a) Apply block diagram reduction to calculate the transfer function. (25 marks)
b) Convert the block diagram into signal flow graph. (15 marks)
2) Using Mason's gain formula, find the transfer function of the following system (30 marks).
3) Solve the below initial value problems using Laplace Transform and calculate Y(s). (30 marks).
3y'' - 5y' + 2y = e^{-2t}, assume zero initial conditions