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Two bars of masses m1 and m2 connected b...

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.

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After releasing the bar 2 acquires the velocity `v_2`, obtained by the energy, conservation:
`1/2m_2v_2^2=1/2kx^2` or, `v_2=xsqrt(k/m_2)` (1)
Thus the sought velocity of C.M.
`v_(cm)=(0+m_2xsqrt((k)/(m_2)))/(m_1+m_2)=(xsqrt(m_2k))/((m_1+m_2))`
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