Multicore ARM how to assign a critical task to one dedicated core
I have worked with NXP LPC4300 series dual core ARM Cortex M chips.

You do not "assign" tasks as you do on a PC. The way you do this is to compile two separate projects, since both cores operate completely independently, apart from the shared bus.  

If you have an multi Cortex A processor you use an operating system to run tasks.
I wouldn't even think about programming these bare metal.