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.

Explanation

As initially `U=overset~U=0`, so, `overset~E=overset~T`
From the solution of
`overset~T=1/2mu|vecv_1-vecv_2|`,
As `vecv_1_|_vecv_2`
Thus `overset~=1/2(m_1m_2)/(m_1+m_2)(v_1^2+v_2^2)`