For undamped single d$.$o$.$f$.$ free vibration system governed by $4u^{\text{'}\text{'}}+16u=0,$ with $u(0)=0$

and $u^{\text{'}}(0)=1\frac{m}{sec}.$ Construct the phase$-$plane diagram using analytical approach and

compare the results using $($i$)$ forward $($ii$)$ backward $($iii$)$ Leap frog, and $($iv$)$ trapezoidal

methods. Assume $t=2\frac{}{8}{}_n$ and calculate the values for the first $10$ values of $t.$ Solve

the problem manually and show the steps in calculation clearly.