which is why I look forward to you posting the results of your attempt AnFI. With the starting point I've given you it's only 4 steps to the standard form of the equation that any rotorcraft engineer would recognise.
Don't forget to state clearly any assumptions and particular notation forms you choose to use. I'd hate to think you'd got it wrong because of the use of different terminology, like centripetal being used to describe a force that acts away from the center of a circle.