Assignment Given: 2x"=-14x+6y and y"=2x-6y +35 sin 4t x(t) = y(t) = x' (t) = y(t) = 0 1. Find the Laplace transforms of the top two equations above, where x(t) and y(t) are the displacement positions (from equilibrium) of masses 1 and 2, respectively, accounting for the boundary conditions given above. 2. Determine the transformed position functions X(w) and Y(w). 3. Determine the inverse transforms of X(w) and Y(w) in order to solve for x(t) and y(t).

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