Radio button value change for hash in Jquery

  <input type="radio" name="search" id="search-vehicle"
        
value="search-vehicle" checked="checked" />Search Vehicle
    &nbsp;&nbsp; 
<input type="radio" name="search" id="search-damages"
        
value="search-damages" /> 

I trying that when come back to for hashing i use following code

      $.history.init(function(hash){
        
if(hash == "") {
        
} else {
           
if(hash=="search-damages"){
               jQuery
("#search-damages-body").show();
               jQuery
("#additional-search-div-main").hide();
               jQuery
("#vehicle-body").hide();
               jQuery
("#margin-div").hide();
               $
('#search-damages')[0].checked = true;
               $
('#search-damages')[0].checked = true;
           
}
     
if(hash =="Addition Search"){
      jQuery
("#additional-search-div-content").toggle();
              jQuery
('#hidden_text').val('Close');
     
}
        
}
    
});

I am try to make radio button value change in case for damage-search it showing me div but radio not change same case happen with addition search do not change value of button.

following code is using for hash

 var value = jQuery('input:radio[name=search]:checked').val();