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I'm a physics tutor. I'm stuck up with this question. I've no clue about how to proceed with this question. Can any one help?

A 2 Kg block moving with 10 m/s strikes a spring of constant π^2 N/m attached to 2 Kg block at rest kept on a smooth floor. The time for which rear moving block remain in contact with spring will be_____?

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closed as too localized by Qmechanic, David Z Feb 18 '12 at 18:27

This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

Hi claws - I would hope you know by now that we expect homework-like questions to ask about concepts, not just ask for solutions or hints for a specific problem. It doesn't matter whether you're a student or a tutor. As usual, I'll be happy to reopen this if you edit it into a conceptual question. – David Z Feb 18 '12 at 18:32
up vote 1 down vote accepted

Switch to a reference frame which moves with the center of mass the system. Consider a point on the spring at the COM of the system. Split the spring into two springs (use the fact that $k\propto 1/l$) at this point. Now, you have a point which is stationary (in com frame), and two blocks attached to it, both of which are vibrating. Find the time period of both oscillations (it'll be the same, $2\pi\sqrt{\frac{m_1}{k_1}}=2\pi\sqrt{\frac{m_2}{k_2}}$), and divide by 2 (since you only want the time in which it completes half a cycle)

Of course, this formula gives the direct answer:$$\text{time period of a two mass-spring system}=2\pi\sqrt{\frac{\mu}{k}}$$, where $\mu=\frac{m_1m_2}{m_1+m_2}$ is the reduced mass.

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It may help to use a frame of reference where the center of mass of the system is at rest.

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