Please see my note book http://mbed.org/users/kenjiArai/notebook/freertos-on-mbed-board-with-mbed-cloud-ide--never-/

This is too old.
Below is another FreeRTOS on mbed.
http://developer.mbed.org/users/rgrover1/code/FreeRTOS/
I don't know it works well or not.
I have not evaluated it.

Revision:
0:d4960fcea8ff
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/FreeRTOS/Common/include/partest.h	Sat Jan 01 11:17:45 2011 +0000
@@ -0,0 +1,100 @@
+/*
+    FreeRTOS V6.0.3 - Copyright (C) 2010 Real Time Engineers Ltd.
+
+    ***************************************************************************
+    *                                                                         *
+    * If you are:                                                             *
+    *                                                                         *
+    *    + New to FreeRTOS,                                                   *
+    *    + Wanting to learn FreeRTOS or multitasking in general quickly       *
+    *    + Looking for basic training,                                        *
+    *    + Wanting to improve your FreeRTOS skills and productivity           *
+    *                                                                         *
+    * then take a look at the FreeRTOS eBook                                  *
+    *                                                                         *
+    *        "Using the FreeRTOS Real Time Kernel - a Practical Guide"        *
+    *                  http://www.FreeRTOS.org/Documentation                  *
+    *                                                                         *
+    * A pdf reference manual is also available.  Both are usually delivered   *
+    * to your inbox within 20 minutes to two hours when purchased between 8am *
+    * and 8pm GMT (although please allow up to 24 hours in case of            *
+    * exceptional circumstances).  Thank you for your support!                *
+    *                                                                         *
+    ***************************************************************************
+
+    This file is part of the FreeRTOS distribution.
+
+    FreeRTOS is free software; you can redistribute it and/or modify it under
+    the terms of the GNU General Public License (version 2) as published by the
+    Free Software Foundation AND MODIFIED BY the FreeRTOS exception.
+    ***NOTE*** The exception to the GPL is included to allow you to distribute
+    a combined work that includes FreeRTOS without being obliged to provide the
+    source code for proprietary components outside of the FreeRTOS kernel.
+    FreeRTOS is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License for
+    more details. You should have received a copy of the GNU General Public 
+    License and the FreeRTOS license exception along with FreeRTOS; if not it 
+    can be viewed here: http://www.freertos.org/a00114.html and also obtained 
+    by writing to Richard Barry, contact details for whom are available on the
+    FreeRTOS WEB site.
+
+    1 tab == 4 spaces!
+
+    http://www.FreeRTOS.org - Documentation, latest information, license and
+    contact details.
+
+    http://www.SafeRTOS.com - A version that is certified for use in safety
+    critical systems.
+
+    http://www.OpenRTOS.com - Commercial support, development, porting,
+    licensing and training services.
+*/
+/*
+ *  Modified for mbed NXP LPC1768 board
+ *  By Kenji Arai / JH1PJL on April 30th,2010
+ *         August 28th, 2010
+ */
+
+#ifndef PARTEST_H
+#define PARTEST_H
+
+#define partstDEFAULT_PORT_ADDRESS        ( ( unsigned short ) 0x378 )
+
+#if (USE_XPRESSO == 1)
+#define LED_1 ( 1UL << 22UL )
+// Dummy only one LED is available
+#define LED_2 ( 0UL << 0UL )
+#define LED_3 ( 0UL << 0UL )
+#define LED_4 ( 0UL << 0UL )
+#else
+#define LED_1 ( 1UL << 18UL )
+#define LED_2 ( 1UL << 20UL )
+#define LED_3 ( 1UL << 21UL )
+#define LED_4 ( 1UL << 23UL )
+#endif
+
+#define REC_SW ( 1UL )
+
+#define partstFIO1_BITS            ( LED_1 | LED_2 | LED_3 | LED_4 )
+#define partstNUM_LEDS            ( 4 )
+
+/* LED */
+#define LED1 0
+#define LED2 1
+#define LED3 2
+#define LED4 3
+#ifdef __cplusplus
+extern "C" {
+#endif
+static unsigned long ulLEDs[] = { LED_1, LED_2, LED_3, LED_4 };
+void vParTestInitialise( void );
+void vParTestSetLED( unsigned portBASE_TYPE, signed portBASE_TYPE );
+void vParTestToggleLED( unsigned portBASE_TYPE );
+unsigned int vParTestSW_Rec( void );
+unsigned int vParTestSW_Mode( void );
+#ifdef __cplusplus
+}
+#endif
+#endif
+