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 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 blocks of masses m_(1) and m_(2) being connected with a light spring of stiffness k are driven with forces F_(1) and F_(2) on a smooth horizontal plane.

Two cubes with masses m_(1) and m_(2) were interconnected by a weightless spring of stiffness x and placed on a smooth horizontal surface. Then the cubes were drawn closer to each other and released simultaneously. Find the natural oscillation frequency of the system.

Two blocks of masses m and M connected by a light spring of stiffness k, are kept on a smooth horizontal surface as shown in figure. What should be the initial compression of the spring so that the system will be about to break off the surface, after releasing the block m_1 ?

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 blocks of masses m_(1) and m_(2) are connected by a massless spring and placed on smooth surface. The spring initially stretched and released. Then :

Two blocks of masses m_(1) and m_(2) interconnect with a spring of stiffness K , are kept on as smooth horizontal surface. Find out the ratio of velocity, displacement, kinetic energy and acceleration block with mass m_(1) of block with mass m_(2) .