Consider the mechanical system shown in the following figure

Consider the mechanical system shown in the following figure, where m_1 and m_2 represent mass, k_1 and k_2 are stiffness coefficients, c is the coefficient of viscous damping, x_1 and x_2 are displacements, and F_1(t) and F_2(t) are the applied forces. Assume, in consistent physical units, the following parameter values m_1 = 1, m_2 = 1, c = 2, k_1 = 1, k_2 = 1, F_1(t) = sin 2t, F_2(t) = e^-t The system\'s equations of motion are then expressed as x_1 + 2x._1 + 2x_1 - x_2 = sin 2t subject to initial conditions x_2 - x_1 + x_2 = e^-t x_1(0) = 0, x_2(0) = 0, x._1(0) = 0, x._2(0) = 0 Transform into a system of first-order IVPs. Write a MATLAB script file that employs the user-defined function RK4System to solve the system in (a). The file must return the plot of x_1 and x_2 versus 0 le t le 6 in the same graph. It is recommended to use at least 100 points for smoothness of curves.

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