b$)$ Using the relationships below transform the equation above into a simple matrix equation for just $3$ positions of the mass. $(x_2,x_3,x_4).$ The initial displacement is $x_0=0\mathrm{.}1m$ and initial velovity $v_0=0\mathrm{.}1\frac{m}{s}.($Hint: this is a parametric question, you only need to assemble the $33$ matrix, no need for inverse$)$

$\frac{d^{2}x}{d{t}^2}$~~$\frac{x_{n+1}-2x_n+x_{n-1}}{t^2}$

$\frac{dx}{dt}$~~$\frac{x_{n+1}-x_n}{t}.$