There are many ways to analyze the vibration of nose landing gear.

You have to decide on the level of detail you want in the model.

Decide how much abstraction can you use and still get the results you want.

For example, you can abstract the tire on the end of the gear as a spring to ground.

Start by describing what you want in the results.  Describe in detail the load history.

At one level of abstraction, you can treat all the parts as rigid bodies connected by joints and spring-dampers. This is the simplest model, but you must know the total mass of each part, including non-structural parts like covers that complete the fairing of the aircraft body.

Next you can let some or all parts be flexible bodies so you can see the stress in those parts. This adds more complexity.

Finally, you can include the tire on the wheel.   Do you want to include the load due to the air speed?

I don't know if there is a brake on the nose gear. I think that is just on the other wheels.