Question

use generalized coordinates to solve

A thin circular cylinder of mass M and radius brests on a perfectly rough horizontal plane, and inside it is placed a perfectly rough sphere of mass m and radius a. If the system be disturbed in a plane perpendicularto the integrals of them; and if the motion be small, show that the length of the simple equivalent pendulum is generators of the cylinder, find the equations of finite motion, and deduce two first 14M (b-a)/ (10M+7m) Find two limits that agree with the motion of the system behaving like a simple pendulum

Answer 1

We have thin circular cylinder mass of cylinder = M radius of cylinder = b A sphere is placed ground it mass of sphere = M radius of sphere = a \r\n length of pendulum is given by angular acceleration = -4 pi^2 F^2 theta therefore F_net = (m + m) d^2 x/dt^2 therefore x (t) = c_1 cos (w t) + c_2 sin (w t) x (t) = A cos (w t - phi) angular frequency w = squareroot k/m velocity of system = dx/dt therefore a (x) = -w^2 x system is in S H M we also know that mg l theta = I alpha l = I alpha/