Two physical pendulums perform small oscillations about the same horizontal axis with frequencies `omega_(1)` and `omega_(2)` . Their moments of inertia relative to the given axis are equal to `I_(1)` and `I_(2)` respectively. In a state of stable equilibium the pendulums were fastened rigifly together. What will be the frequency of small oscillations of the compound pendulum ?

A physical pendulum performs small oscillations about the horizontal axis with frequency omega_(1)=15.0 s^(-1) . When a small body of mass m=50 g is fixed to the pendulum at a distance l=20 cm below the axis, the oscillation frequency becomes equal to omega_(2)=10.0 s^(-1) . Find the moment of inertia of the pendulum relative to the oscillation axis.

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) .

Two independent harmonic oscillators of equal mass are oscillating about the origin with angular frequencies omega_(1) and omega_(2) and have total energies E_(1) and E_(2) repsectively. The variations of their momenta p with positions x are shown in figures. If (a)/(b) = n^(2) and (a)/(R) = n , then the correc t equation(s) is (are) :

Two independent harmonic oscillators of equal mass are oscillating about the origin with angular frequencies omega_(1) and omega_(2) and have total energies E_(1) and E_(2) repsectively. The variations of their momenta p with positions x are shown in figures. If (a)/(b) = n^(2) and (a)/(R) = n , then the correc t equation(s) is (are) :

Two horizontal discs rotate freely about a vertical axis passing through their centres. The moments of inertia of the discs relative to this axis are equal to I_1 and I_2 , and the angular velocities to omega_1 and omega_2 . When the upper disc fell on the lower one, both discs began rotating, after some time, as a single whole (due to friction). Find: (a) teh steady-state angular rotation velocity of the discs, (b) the work performed by the friction forces in this process.

Find the frequency of small oscillations of the arrangement illustrated in figure. The radius of the pulley is R , its moment of inertia relative to the rotation axis is I , the mass of the body is m , and the spring stiffness is x .The mass of the thread and the spring is negligible , the thread does not slide over the pulley, there is no friction in the axis of the pulley

A wave of angular frequency omega propagates so that a certain phase of oscillation moves along x-axis, y-axis, z-axis with speeds c_(1) c_(2) and c_(3) respectively.