This　paper　presents　a　hybrid　static　output　feedback　stabilization　approach　for　harmonic　oscillating　systems,　which　are　not　stabilizable　via　a　static　output　feedback.　More　precisely,　we　find　two　output　feedback　gains　and　a　switching　law　orchestrating　the　feedback　gains　such　that　the　closed-loop　system　is　asymptotically　stable.　It　is　shown　that　stability　conditions　can　be　met　with　respect　to　the　discrete　state　when　the　switched　system＇s　stabilization　theorem　is　used.