Two small discs of masses `m_1` and `m_2` interconnected by a weightless spring rest on a smooth horizontal plane. The discs are set in motion with initial velocities `v_1` and `v_2` whose directions are mutually perpendicular and lie in a horizontal plane. Find the total energy `overset~E` of this system in the frame of the centre of inertia.

Two small discs of masses m_(1) and m_(2) are connected by a weightless spring resting on a smooth horizontal plance. The discs are set in motion with initial velocities v_(1) and v_(2) whose directions are mutually perpendicular and in the same horizontal plane. Find the total energy E of hte system with reference to the frame fixed to the centre of mass.

Two small discs of masses m_(1) and m_(2) are connected by a weightless spring resting on a smooth horizontal plance. The discs are set in motion with initial velocities v_(1) and v_(2) whose directions are mutually perpendicular and in the same horizontal plane. Find the total energy E of hte system with reference to the frame fixed to the centre of mass.

A system consists of two small spheres of masses m_1 and m_2 interconnected by a weightless spring. At the moment t=0 the spheres are set in motion with the initial velocities v_1 and v_2 after which the system starts moving in the Earth's uniform gravitational field. Neglecting the air drag, find the time dependence of the total momentum of this system in the process of motion and of the radius vector of its centre of inertia relative to the initial position of the centre.

Two cubes of mass m_(1) and m_(2) are interconnected by a weightless spring of stiffness k and placed on a smooth horizontal table. Then the cubes are drawn closer to each other and released. Find the frequency of oscillation.

Two bars of masses m_1 and m_2 connected by a weightless spring of stiffness ϰ (figure) rest on a smooth horizontal plane. Bar 2 is shifted a small distance x to the left and then released. Find the velocity of the centre of inertia of the system after bar 1 breaks off the wall.

Two bars of masses m_1 and m_2 connected by a weightless spring of stiffness k , rest on a smooth horizontal plane. Bar 2 is shifted by a small distance x_0 to the left and released. The veloicyt of the centre of mass of the system when bar 1 breaks off the wall is

Two bars of masses m_1 and m_2 connected by a weightless spring of stiffness k , rest on a smooth horizontal plane. Bar 2 is shifted by a small distance x_0 to the left and released. The veloicyt of the centre of mass of the system when bar 1 breaks off the wall is

Two blocks of masses m_(1) and m_(2) , connected by a weightless spring of stiffness k rest on a smooth horizontal plane as shown in Fig. Block 2 is shifted a small distance x to the left and then released. Find the velocity of centre of mass of the system after block 1 breaks off the wall.