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    Represent the two systems of differential equations in matrix form; Where denotes the second order differential equation of displacement, u with respect to time, t When m=1 and k=1; Try a solution of the form; Where denotes the angular frequency Differentiate twice (C3.6; M1.1; FP2.7) Substitute into system of equations (FP1.4; The exact solution of the ordinary differential equation is given by . The solution to this nonlinear equation at weeks is. Figure 1 compares the exact solution with the numerical solution from Euler’s method for the step size of. Figure 1. Comparing exact and Euler’s method. The problem was solved again using smaller step sizes.

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    transforms in the areas of science and engineering. At flrst, simple application in the area of Physics and Elec- applying laplace transform to this equation, let Represent the two systems of differential equations in matrix form; Where denotes the second order differential equation of displacement, u with respect to time, t When m=1 and k=1; Try a solution of the form; Where denotes the angular frequency Differentiate twice (C3.6; M1.1; FP2.7) Substitute into system of equations (FP1.4;