Problem 1.287

A cylindrical disc of a gyroscope of mass \(m=15 \mathrm{~kg}\) and radius \(r=5.0 \mathrm{~cm}\) spins with an angular velocity \(\omega=330 \mathrm{rad} / \mathrm{s}\) The distance between the bearings in which the axle of the disc is mounted is equal to \(l=15 \mathrm{~cm} .\) The axle is forced to oscillate about a horizontal axis with a period \(T=1.0 \mathrm{~s}\) and amplitude \(\varphi_{m}=20^{\circ}\) Find the maximum value of the gyroscopic forces exerted by the axle on the bearings.