The solution of the forced Mass$-$Spring$-$Damper with the following parameters

m$=1320$m$=1320$ kg$,$ c$=7920$c$=7920$ Ns$/$m$,$ k$=81200$k$=81200$ N$/$m$,$ undergoing forcing function F$($t$)=5400$cos$(4$t$)$F$($t$)=5400$cos$(4$t$)$

takes the form

x$($t$)=$e$3$t$($A$1$cos$(7\mathrm{.}2467$t$)+$A$2$sin$(7\mathrm{.}2467$t$))+0\mathrm{.}0795$cos$(4$t$0\mathrm{.}4852)$x$($t$)=$e$3$t$($A$1$cos$(7\mathrm{.}2467$t$)+$A$2$sin$(7\mathrm{.}2467$t$))+0\mathrm{.}0795$cos$(4$t$0\mathrm{.}4852).$

Note that $0(3)$$0(3),$ d$(7\mathrm{.}2467)$d$(7\mathrm{.}2467),$ A$(0\mathrm{.}0795)$A$(0\mathrm{.}0795)$ and $(0\mathrm{.}4852)$$(0\mathrm{.}4852)$ have already been determined.

Given the initial conditions:

x$(0)=0\mathrm{.}02$x$(0)=0\mathrm{.}02$m and $$x$(0)=4$x$(0)=4$m$/$s

find the exact solution.

Enter your answers for A$1$A$1$ and A$2$A$2$ to four decimal places in the appropriate boxes below:

A$1$:A$1$:

A$2$:A$2$: