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Two masses and are attached by a spring of spring constant and of relaxed length .
They move freely on a horizontal axis (x'x) without friction.
When , the spring is relaxed, the masses and are at rest on and .
From , a horizontal constant force is exerted on .
Let and .
Find and .
We apply the second law of Newton on each of the two masses, we project it on the axis (Ox) :
We sum the equations :
We integrate and take the initial values into account :
We can write the equations as :
By subtracting these equations :
We note :
The solution is :
Using the initial values :
From which we deduce and , since we know their sum and their difference.