- #1
erisedk
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Homework Statement
Two point masses m1 and m2 are coupled by a spring of spring constant k and uncompressed length L0. 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 v0. 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 x1 (t) = v0t - A(1-cos(ωt)) where A is a constant. Find (i) the displacement x2(t) of mass m2, and (ii) the relationship between A and L0.
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.