Two swings are hanging from a 3 meter rectangular wood beam embedded at both ends. Swing 1 is attached at x = 1 m and swing 2 is attached at x = 2 m. The person on swing 1 applies a point force of A Newton and the person on swing 2 applies a point force of B newton downwards. The differential equation is y'=A8(x-1) + B8( B8(x-2) with the four boundary conditions y(0) = 0 and y'(0) = 0 y"(0) = P and y'" (0) = Q. Determine the deflection of the beam as a function of x in terms of A, B, E, I, P and Q using the Laplace transform. Express your solution as a piecewise function. 9.1 Applying the Laplace transform, will result in the expression for L{y} term 2 term 3 term 1 P term 4 L{y} Q e918- B 1 920 (s**) (5917) EI (s**) EI (19) 9.2 Term 1 can be expressed as L{P 9211"} 9.3 Term 4 can be expressed as LB 922 (1 − 923) ¹24 H (1 - ** -**)} 9.4 In expressing the solution y as a piecewise function, the part corresponding to the interval 1 < x < 2 has non zero terms: y(x) =P**+ Q** ... 925 = 0 y(x) =P**+Q**+ ... 925 = 1 y(x) =P**+ Q ** + A ** ... 925 = 2 **