現在の日付がある週の月曜日の日付を検索します.

var now = new Date();
var monday = now;
monday.setDate(now.getDate() - now.getDay() + 1);
monday_date = monday.getFullYear() + "-" + monday.getMonth() + "-" + monday.getDate();

now = new Date();
var sunday = new Date();
sunday.setDate(now.getDate() - now.getDay() + 7);
monday_date = sunday.getFullYear() + "-" + sunday.getMonth() + "-" + sunday.getDate();

monday_date = Date.today.beginning_of_week.strftime('%d/%m/%Y')