Remaining "How Did I Do$?"$ Uses: $\backslash (2/3\backslash )$

Consider a simple harmonic oscillator that consists of a $1\mathrm{.}2$ kg mass connected to a spring with a force constant of $\backslash (165\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$m$\}\backslash ).$ The oscillator is placed horizontally on a table with a static coefficient of friction $\backslash (\backslash$mu$\_\{\backslash$mathrm$\{$S$\}\}=0\mathrm{.}15\backslash )$ and a kinetic coefficient of friction of $\backslash (\backslash$mu$\_\{\backslash$mathrm$\{$K$\}\}=0\mathrm{.}07\backslash ).$

$($a$)$ One end of the spring is free for you to push$/$pull$.$ If you push$/$pull a small amount, the mass will not move. If you push$/$pull over a threshold value, the mass will begin to move. How far can the spring be stretched without moving the mass?

$($b$)$ The mass is now made to oscillate at double the amplitude found in part $($a$).$ What total distance does the mass travel before stopping? Assume it starts with the maximum amplitude. Hint: Conserve energy. There is an example in the chapter of the book that may provide some guidance on how to do this.