There are many questions/answers available here to understand Ramp up time but I want to get something in detail for my test case.
Test Case
You should use the Ultimate Thread Group plugins available in Standard set.
To maintain concurrency the configuration should be like this:
Start Thread Count: 1200
Initial delay, sec: 0
Startup, sec: 60
Hold Load: 180
Shutdown Time, sec: 60
Ultimate Thread Group
Here all the 1200 threads will be generated and up within 60 sec of Startup time(Ramp up time) .Those 1200 threads will be active for next 180 sec, and after that, those threads will shut down within next 60 sec.
So overall duration of the test is 300 sec as you desire. Throughout the Hold Load time(180sec) the requests will be looped.
This ultimate thread group will give you more control over Threads.
Now if you want to control the rate of transactions per second or the number of samples to execute you can use Constant Throughput Timer. Constant Throughput Timer will let you control the flow of requests to be sent. The default "Thread Group" only control the way the users or threads will be generated.It doesn't control the rate of requests to be hit your application.So for this purpose, you could use "Constant Throughput Timer" to control your requests per second. For further detail, you could go through JMeter documentation.