An arrangedment illlustrated in figure consists of a horizontal uniform disc `D` of mass `m` and radius `R` and a thin rod `AO` whose torsional coefficient is equal to `k`. Find the amplitude and the energy of small torsional oscillationa if at the initial momentu the disc was deviated through an angle `varphi_(0)` from the equilibrium position and then imparted an angular velocity `varphi_(0)`.

A uniform rod of mass m and length l performs small oscillations about the horizontal axis passing throughits upper end. Final the mean kinetic energy of the rod averaged over one oscillation period it at the initial mment it was deflected from the vertical by an angle theta_(0) and then imparted an angular velocity theta_(0) .

Find the elastic deformation energy of a steel rod whose one end is fixed and the other is twisted through an angle varphi=6.0^@ . The length of the rod is equal to l=1.0m , and the radius to r=10mm .

A uniform disc of mass m and radius R is pivoted at point P and is free rotate in vertical plane. The centre C of disc is initially in horizontal position with P as shown in figure. If it is released from this position, then its angular acceleration when the line PC is inclined to the horizontal at an angle theta is

A uniform rod of mass m and length l is suspended through a light wire of length l and torsional constant k as shown in figure. Find the time perid iof the system makes a. small oscillations in the vertical plane about the suspension point and b. angular oscillations in the horizontal plane about the centre of the rod.

A uniform rod of mass m and length l is suspended through a light wire of length l and torsional constant k as shown in figure. Find the time perid iof the system makes a. small oscillations in the vertical plane about the suspension point and b. angular oscillations in the horizontal plane about the centre of the rod.

Find the period of small torsional oscillational of a system consisting of two discs slipped oon a thin rod with rod with torsional coefficient k . The moments of inertia of discs relative to the rod's axis are equal to I_(1) and I_(2) .

A man of mass m_1 stands on the edge of a horizontal uniform disc of mass m_2 and radius R which is capable of rotating freely about a stationary vertical axis passing through its centre. At a certain moment the man starts moving along the edge of the disc, he shifts over an angle varphi^' relative to the disc and then stops. In the process of motion the velocity of the man varies with time as v^'(t) . Assuming the dimensions of the man to be negligible, find: (a) the angle through which the disc had turned by the moment the man stopped, (b) the force moment (relative to the rotation axis) with which the man acted on the disc in the process of motion.

A uniform disc of mass m and radius R is pivoted smoothly at its centre of mass. A light spring of stiffness k is attached with the dics tangentially as shown in the Fig. Find the angular frequency in (rad)/(s) of torsional oscillation of the disc. (Take m=5kg and K=10(N)/(m) .)