Laplace transform rotational mechanical system
You have 2 linear state variable equations. Laplace transform both sides of both of them. Eliminate the Laplace transform of w1. Calculate the ratio of the Laplace transforms of w2 and the input torque. You may need to assume that the system starts from rest to fade the initial angular velocity.
BTW. the state variable equations are useful as is if you know the constants as numerical values. You can in that case simulate the system even with a circuit analyzer or a spreadsheet.