Notice: Only variables should be assigned by reference in /var/www/html/phy.tw/plugins/system/jsecurelite/jsecurelite.php on line 19

Notice: Only variables should be assigned by reference in /var/www/html/phy.tw/plugins/system/jsecurelite/jsecurelite.php on line 40
單擺與錐擺

Warning: Illegal string offset 'type' in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 691

Warning: Illegal string offset 'options' in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 702

Notice: Array to string conversion in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 702

Warning: Illegal string offset 'type' in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 691

Warning: array_replace(): Expected parameter 1 to be an array, string given in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 694

Warning: Illegal string offset 'relative' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 626

Warning: Cannot assign an empty string to a string offset in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 626

Warning: Illegal string offset 'pathOnly' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 627

Warning: Cannot assign an empty string to a string offset in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 627

Warning: Illegal string offset 'detectBrowser' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 628

Warning: Illegal string offset 'detectDebug' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 629

Warning: Illegal string offset 'relative' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 632

Warning: Illegal string offset 'detectBrowser' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 632

Warning: Illegal string offset 'detectDebug' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 632

Warning: Illegal string offset 'pathOnly' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 635

Warning: Illegal string offset 'type' in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 691

Warning: array_replace(): Expected parameter 2 to be an array, string given in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 694

Warning: Illegal string offset 'relative' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 626

Warning: Cannot assign an empty string to a string offset in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 626

Warning: Illegal string offset 'pathOnly' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 627

Warning: Cannot assign an empty string to a string offset in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 627

Warning: Illegal string offset 'detectBrowser' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 628

Warning: Illegal string offset 'detectDebug' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 629

Warning: Illegal string offset 'relative' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 632

Warning: Illegal string offset 'detectBrowser' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 632

Warning: Illegal string offset 'detectDebug' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 632

Warning: Illegal string offset 'pathOnly' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 635

Warning: Illegal string offset 'type' in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 691

Warning: array_replace(): Expected parameter 2 to be an array, string given in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 694

Warning: Illegal string offset 'relative' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 626

Warning: Cannot assign an empty string to a string offset in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 626

Warning: Illegal string offset 'pathOnly' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 627

Warning: Cannot assign an empty string to a string offset in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 627

Warning: Illegal string offset 'detectBrowser' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 628

Warning: Illegal string offset 'detectDebug' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 629

Warning: Illegal string offset 'relative' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 632

Warning: Illegal string offset 'detectBrowser' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 632

Warning: Illegal string offset 'detectDebug' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 632

Warning: Illegal string offset 'pathOnly' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 635

Warning: Illegal string offset 'type' in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 691

Warning: array_replace(): Expected parameter 2 to be an array, string given in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 694

Warning: Illegal string offset 'type' in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 691

Warning: array_replace(): Expected parameter 2 to be an array, string given in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 694

Warning: Illegal string offset 'type' in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 691

Warning: array_replace(): Expected parameter 2 to be an array, string given in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 694

Warning: Illegal string offset 'type' in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 691

Warning: array_replace(): Expected parameter 2 to be an array, string given in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 694

Warning: Illegal string offset 'type' in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 691

Warning: array_replace(): Expected parameter 2 to be an array, string given in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 694

Warning: Illegal string offset 'type' in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 691

Warning: array_replace(): Expected parameter 2 to be an array, string given in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 694

Warning: Illegal string offset 'type' in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 691

Warning: array_replace(): Expected parameter 2 to be an array, string given in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 694

Warning: Illegal string offset 'relative' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 626

Warning: Cannot assign an empty string to a string offset in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 626

Warning: Illegal string offset 'pathOnly' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 627

Warning: Cannot assign an empty string to a string offset in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 627

Warning: Illegal string offset 'detectBrowser' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 628

Warning: Illegal string offset 'detectDebug' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 629

Warning: Illegal string offset 'relative' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 632

Warning: Illegal string offset 'detectBrowser' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 632

Warning: Illegal string offset 'detectDebug' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 632

Warning: Illegal string offset 'pathOnly' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 635

Warning: Illegal string offset 'type' in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 691

Warning: array_replace(): Expected parameter 2 to be an array, string given in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 694

Warning: Illegal string offset 'relative' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 626

Warning: Cannot assign an empty string to a string offset in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 626

Warning: Illegal string offset 'pathOnly' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 627

Warning: Cannot assign an empty string to a string offset in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 627

Warning: Illegal string offset 'detectBrowser' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 628

Warning: Illegal string offset 'detectDebug' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 629

Warning: Illegal string offset 'relative' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 632

Warning: Illegal string offset 'detectBrowser' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 632

Warning: Illegal string offset 'detectDebug' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 632

Warning: Illegal string offset 'pathOnly' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 635

Warning: Illegal string offset 'type' in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 691

Warning: array_replace(): Expected parameter 2 to be an array, string given in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 694

Warning: Illegal string offset 'type' in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 691

Warning: array_replace(): Expected parameter 2 to be an array, string given in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 694

Warning: Illegal string offset 'type' in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 691

Warning: array_replace(): Expected parameter 2 to be an array, string given in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 694

Warning: Illegal string offset 'type' in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 691

Warning: array_replace(): Expected parameter 2 to be an array, string given in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 694

Warning: Illegal string offset 'type' in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 691

Warning: array_replace(): Expected parameter 2 to be an array, string given in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 694

Warning: Illegal string offset 'type' in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 691

Warning: array_replace(): Expected parameter 2 to be an array, string given in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 694

Warning: Illegal string offset 'type' in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 691

Warning: array_replace(): Expected parameter 2 to be an array, string given in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 694

Warning: Illegal string offset 'type' in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 691

Warning: array_replace(): Expected parameter 2 to be an array, string given in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 694

Warning: Illegal string offset 'relative' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 626

Warning: Cannot assign an empty string to a string offset in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 626

Warning: Illegal string offset 'pathOnly' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 627

Warning: Cannot assign an empty string to a string offset in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 627

Warning: Illegal string offset 'detectBrowser' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 628

Warning: Illegal string offset 'detectDebug' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 629

Warning: Illegal string offset 'relative' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 632

Warning: Illegal string offset 'detectBrowser' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 632

Warning: Illegal string offset 'detectDebug' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 632

Warning: Illegal string offset 'pathOnly' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 635

Warning: Illegal string offset 'type' in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 691

Warning: array_replace(): Expected parameter 2 to be an array, string given in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 694

Warning: Illegal string offset 'relative' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 626

Warning: Cannot assign an empty string to a string offset in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 626

Warning: Illegal string offset 'pathOnly' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 627

Warning: Cannot assign an empty string to a string offset in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 627

Warning: Illegal string offset 'detectBrowser' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 628

Warning: Illegal string offset 'detectDebug' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 629

Warning: Illegal string offset 'relative' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 632

Warning: Illegal string offset 'detectBrowser' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 632

Warning: Illegal string offset 'detectDebug' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 632

Warning: Illegal string offset 'pathOnly' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 635

Warning: Illegal string offset 'type' in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 691

Warning: array_replace(): Expected parameter 2 to be an array, string given in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 694

Warning: Illegal string offset 'relative' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 626

Warning: Cannot assign an empty string to a string offset in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 626

Warning: Illegal string offset 'pathOnly' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 627

Warning: Cannot assign an empty string to a string offset in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 627

Warning: Illegal string offset 'detectBrowser' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 628

Warning: Illegal string offset 'detectDebug' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 629

Warning: Illegal string offset 'relative' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 632

Warning: Illegal string offset 'detectBrowser' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 632

Warning: Illegal string offset 'detectDebug' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 632

Warning: Illegal string offset 'pathOnly' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 635

Warning: Illegal string offset 'type' in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 691

Warning: array_replace(): Expected parameter 2 to be an array, string given in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 694

Warning: Illegal string offset 'type' in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 691

Warning: array_replace(): Expected parameter 2 to be an array, string given in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 694

Warning: Illegal string offset 'type' in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 691

Warning: array_replace(): Expected parameter 2 to be an array, string given in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 694

Warning: Illegal string offset 'type' in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 691

Warning: array_replace(): Expected parameter 2 to be an array, string given in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 694

Warning: Illegal string offset 'type' in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 691

Warning: array_replace(): Expected parameter 2 to be an array, string given in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 694

Warning: Illegal string offset 'type' in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 691

Warning: array_replace(): Expected parameter 2 to be an array, string given in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 694

Warning: Illegal string offset 'type' in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 691

Warning: array_replace(): Expected parameter 2 to be an array, string given in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 694

Warning: Illegal string offset 'relative' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 626

Warning: Cannot assign an empty string to a string offset in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 626

Warning: Illegal string offset 'pathOnly' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 627

Warning: Cannot assign an empty string to a string offset in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 627

Warning: Illegal string offset 'detectBrowser' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 628

Warning: Illegal string offset 'detectDebug' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 629

Warning: Illegal string offset 'relative' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 632

Warning: Illegal string offset 'detectBrowser' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 632

Warning: Illegal string offset 'detectDebug' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 632

Warning: Illegal string offset 'pathOnly' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 635

Warning: Illegal string offset 'type' in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 691

Warning: array_replace(): Expected parameter 2 to be an array, string given in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 694

Warning: Illegal string offset 'relative' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 626

Warning: Cannot assign an empty string to a string offset in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 626

Warning: Illegal string offset 'pathOnly' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 627

Warning: Cannot assign an empty string to a string offset in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 627

Warning: Illegal string offset 'detectBrowser' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 628

Warning: Illegal string offset 'detectDebug' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 629

Warning: Illegal string offset 'relative' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 632

Warning: Illegal string offset 'detectBrowser' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 632

Warning: Illegal string offset 'detectDebug' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 632

Warning: Illegal string offset 'pathOnly' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 635

Warning: Illegal string offset 'type' in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 691

Warning: array_replace(): Expected parameter 2 to be an array, string given in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 694

Warning: Illegal string offset 'relative' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 626

Warning: Cannot assign an empty string to a string offset in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 626

Warning: Illegal string offset 'pathOnly' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 627

Warning: Cannot assign an empty string to a string offset in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 627

Warning: Illegal string offset 'detectBrowser' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 628

Warning: Illegal string offset 'detectDebug' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 629

Warning: Illegal string offset 'relative' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 632

Warning: Illegal string offset 'detectBrowser' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 632

Warning: Illegal string offset 'detectDebug' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 632

Warning: Illegal string offset 'pathOnly' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 635

Warning: Illegal string offset 'type' in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 691

Warning: array_replace(): Expected parameter 2 to be an array, string given in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 694

Warning: Illegal string offset 'type' in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 691

Warning: array_replace(): Expected parameter 2 to be an array, string given in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 694

Warning: Illegal string offset 'type' in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 691

Warning: array_replace(): Expected parameter 2 to be an array, string given in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 694

Warning: Illegal string offset 'type' in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 691

Warning: array_replace(): Expected parameter 2 to be an array, string given in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 694

Warning: Illegal string offset 'type' in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 691

Warning: array_replace(): Expected parameter 2 to be an array, string given in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 694

Warning: Illegal string offset 'type' in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 691

Warning: array_replace(): Expected parameter 2 to be an array, string given in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 694

Warning: Illegal string offset 'type' in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 691

Warning: array_replace(): Expected parameter 2 to be an array, string given in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 694

Warning: Illegal string offset 'relative' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 626

Warning: Cannot assign an empty string to a string offset in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 626

Warning: Illegal string offset 'pathOnly' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 627

Warning: Cannot assign an empty string to a string offset in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 627

Warning: Illegal string offset 'detectBrowser' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 628

Warning: Illegal string offset 'detectDebug' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 629

Warning: Illegal string offset 'relative' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 632

Warning: Illegal string offset 'detectBrowser' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 632

Warning: Illegal string offset 'detectDebug' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 632

Warning: Illegal string offset 'pathOnly' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 635

Warning: Illegal string offset 'type' in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 691

Warning: array_replace(): Expected parameter 2 to be an array, string given in /var/www/html/phy.tw/libraries/src/Document/Document.php on line 694

Warning: Illegal string offset 'relative' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 626

Warning: Cannot assign an empty string to a string offset in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 626

Warning: Illegal string offset 'pathOnly' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 627

Warning: Cannot assign an empty string to a string offset in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 627

Warning: Illegal string offset 'detectBrowser' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 628

Warning: Illegal string offset 'detectDebug' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 629

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Warning: Illegal string offset 'detectBrowser' in /var/www/html/phy.tw/libraries/src/HTML/HTMLHelper.php on line 632

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單擺與錐擺

單擺與錐擺

目的

探討單擺與錐擺的週期關係。


實驗

探討單擺與錐擺的週期關係。

 


原理思考

為何擺動路徑較長的錐擺,其週期亦較長?

 

單擺運動的週期與擺長、重力加速度有關(無關擺錘質量),其週期公式為

其中為單擺周期、為單擺擺長、為重力加速度。 而錐擺的轉動周期會與角度(錐擺角度)有關,如公式如下: 

其中為錐擺周期、為錐擺擺長、為錐擺與鉛直線的夾角,為重力加速度。如圖示

由以上探討得知,錐擺的週期較短。

fig11

 

問題討論

造成本實驗尚有哪些因素?

 

1. 未考慮週期在非小角度下擺動的修正。

2. 因為空氣阻力導致的阻尼效應。 

 

關於實驗

1.本實驗於2009全國物理教學及示範研討會中發表。

2.論文壁報內容如附件

3.可同本網站中的實驗D43.依斯克里奇擺做比較。

 

參考資料

"University Physics (John Wiley and sons , inc. 1995) , revised , chap.6., Harris Benson

  

製作

高聖琦

 

指導老師

朱慶琪

 

撰稿

高聖琦 

 

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