# Role of the fly-wheel in a fatigue test of a damper

I would like to build a system to carry out a fatigue test of a damper. I am not able to understand the role of the fly-wheel in such a system. The base idea is a crank-shaft mechanism which has a constant angular velocity and moves the damper along a sinusoidal. The required torque is sinusoidal as well, it oscillates between 0 and a maximum value. When I try to imagine the process, I think the fly-wheel can't help since we just need more work to keep the energy of the fly-wheel constant. The parameters: $$Force: F_{max}=13000N\\ Angular\ velocity:\omega=10\ s^{-1}\\ Amplitude:A=0.01\ m\\ fly-wheel\ moment\ of\ inertia: Θ=2$$ From the force and the velocity I calculated a damping constant: $$b=130000\frac{Ns}{m}$$.The next idea was to check how does the system work without any input, after a certain starting angular velocity. I made the following equation, and checked how the system slows down in time. $$\frac{d\omega (t)}{dt}=\frac{-b\ A^2\ \omega (t)\ sin^2(\omega (t) t)}{Θ}$$ I can see, a bigger fly-wheel can store more energy, and let the system work longer without any input torque. But when I would like to maintain the angular velocity (or the energy) of the constant, I do not see, how can a fly-wheel help the work of the motor which inputs the required torque into the system. Can you give me an intuition to understand the role of the fly-wheel in such a system?