* (c) Write out the equivalent ladder logic programs for the following: i. Boolean expression: ((X000X001)(X002+X003))+X004=Y000 ii. Truth Table (5 marks) * (d) Identify and explain the operation of the ladder logic in Figure Q1 (d). How is this different from the use of a Conditional Jump command? (e) Explain the operation of the ladder logic in Figure Q1 (e). Implement an alternative ladder logic method to achieve the same functionality. (5 marks) Figure Q1 (e) (f) Explain, with the aid of a diagram, the following performance measurements for second order control system models: i. Rise Time ii. Overshoot iii. Settling Time (5 marks) * (g) A first-order system has a time constant of 4 seconds and a steady-state transfer function of 6 . What is the form of the differential equation for this system and its solution? (5 marks) (h) With the aid of diagrams, explain what you understand by the terms 'damping' and 'damping ratio () ' with regard to a second order control system (massspring-damper) subjected to a step input F, as described by the following differential equation. How is calculated in terms of m,c and k values? mdt2d2x+cdtdx+kx=F