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.