How to update the folder property in sharepoint shareddocument folder - powershell

Question

Below C# code I have used to update the folder property in shared document, same concept I have tried in PowerShell but I didn't get any clue.
SPFolder newFolder = folders.Add(ParentURL + FolderURL + "/" + FolderName);
//Added Title Property to newFolder
newFolder.AddProperty("vti_title", FolderName);
//newFolder.Update();
In PowerShell:
> $web = Get-SPWeb "http://server/sites/4tmdk9h7qc4g"
> $site=$web $list = $web.Lists["Shared Documents"]
foreach ($item in $list.Folders)
{
write-host $item["Title"]
/?? HOW TO UPDATE HERE
$item.Update()
}

Answer 1

$item is a SPListItem object. Use SPListItem.Folder to access the SPFolder object:
$item.Folder

Answer 2

Finally this code loop all the site document folder and updated the title
$inputUrl =Read-Host "Enter the site URL"
$site = Get-SPSite -identity $inputUrl
$site | Get-SPWeb -limit |ForEach-Object
{
$web = Get-SPWeb $_.Url
$list =$web.lists["Shared Documents"]
Write-Host $_.Url
foreach($item in $list.folders)
{
$item["Title"]="ayyappan"
$item.update()
Write-Host $item["Title"]
}
}