A ring of mass `m` is attached to a horizontal spring of spring constant `k` and natural length `l_0`. The other end of the spring is fixed and the ring can slide on a horizontal rod as shown. Now the ring is shifted to position B and released Find the speed of the ring when the spring attains its natural length.

Explanation

Let the extension of spring is `x` when the ring is in position B.
`cos53^@=(l_0)/(l_0+x)implies(3)/(5)=(l_0)/(l_0+x)impliesx=(2l_0)/(3)`
Between B and A
`(1)/(2)kx^2=(1)/(2)mv^2`
`v=xsqrt((k)/(m)()=(2l_0)/(3)sqrt((k)/(m))`