Question

4. Refer to the graph as shown in Figure A4, determine (a) the second moment of area about x axis (Ix): (4 marks) (b) the second moment of area about y axis (Iy); (4 marks) c) the second moment of area of about z (Iz), where z axis is perpendicular to x and y axes. (2 marks) 5 y = 1.25x X 4 Figure A4 5. 1 Given the differential equation: dy +-y 3x2 dx х Find (a) the general solution for the differential equation; and (6 marks) (b) the particular solution for the differential equation if the boundary condition is y(1) =2. (2 marks) 6. (a) Determine the Laplace transform of the function f(t) = 4sin3t+e-2t cos4t. (4 marks) 1 1 (b) Determine the inverse Laplace transform of the function F(s) = + s+3 $2+25 (4 marks)

Answer 1

Ó 7 6. niven, flt) = usingt + e-t cosut Taleing aplocce franyforom both sides, we get Llflt)) L (usinat) + Llezt cosut) (8+2) 8² +3² LIFID)) = + (8+2) 8² +9 18+3)+16 A u x 3 + (8+2) ²7 42 12

+ al (18) = e 3t bi f18)= 843 Taking inverße loplace transform both sides, we get L-(+18)) = (X+3) + 602795) L! LI + 5