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## Homework Statement

Two point masses m1 and m2 are coupled by a spring of spring constant k and uncompressed length L

_{0}. The spring is fully compressed and a thread ties the masses together with negligible separation between them. The tied assembly is moving in the +x direction with uniform speed v

_{0}. At a time, say t = 0, it is passing the origin and at that instant the thread breaks. The masses, attached to the spring, start oscillating. The displacement of mass m1 is given by x

_{1}(t) = v

_{0}t - A(1-cos(ωt)) where A is a constant. Find (i) the displacement x

_{2}(t) of mass m2, and (ii) the relationship between A and L

_{0}.

## Homework Equations

## The Attempt at a Solution

First part is easy. Using

##x_{cm} = \dfrac{m_1x_1 + m_2x_2}{m_1 + m_2}##

and substituting ##x_{cm} = v_0t## and ##x_1= v_0t - A(1-\cos{ωt})##

we get ##x_2 = v_0t + \dfrac{m_1}{m_2}.A(1-\cos{wt})##

However, I'm not sure what to do for part (ii). I suppose it involves using the energy equation, but that isn't really working out because of the ##t## (time). I think we might have to minimise or maximise something, in any case, I'm not sure how to proceed. Please help.