Continuing with the system of differential equations from Problem #$2,$ as the force of friction increases $($so that lambda increases$)$ the system will eventually reach a state where it is critically damped, and then overdamped.

Take your solution to problem #$2$ and put it into a while loop where the parameter containing friction, $,$ will increase by $0\mathrm{.}02$ each iteration. Each iteration, check to see whether the displacement x$($t$)$ becomes negative AT ANY POINT IN TIME between t $=0$ and $$t $=5.$ Exit the while loop the first time that you reach a value of where x$($t$)$ is never negative on $[0,5].$ What is that numerical value of obtained from your program $($to two decimal places$)?$