Consider a linear time invariant system described by the following di

erence equation: y$[$n$]=14($x$[$n$]+2$x$[$n $1]+$ x$[$n $2])1.$ Suppose for an input sequence x$1[$n$]=$ cos $(!0$n$)$ with $0!0<2,$ the output sequence is y$1[$n$]=0$ for all n$.$ Find $!0.2.$ If the input is x$2[$n$]=$ cos $$n $2,$ determine the output sequence y$2[$n$]$ in its simplest possible form