Q$14.$ Figure below shows two waves in a rope approaching each other at instant $t=0.$ For any instant after $t=0,$ determine the maximum displacement that occurs given that the big peak has amplitude of $0\mathrm{.}2$ m and the small one has an amplitude of $0\mathrm{.}1$ m $($hint: justify your answers$)$

$($a$)$ at $x=0m,$

$($b$)$ at $x=0\mathrm{.}90m$

$($c$)$ anywhere along the rope