(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I want to find the equations of motion of two masses [itex]m_1[/itex] and [itex]m_2[/itex] attached to each other by a spring on a smooth surface assuming [itex]m_2[/itex] is given an instantaneous velocity [itex]v_0[/itex] at time zero. Call the unstretched length of the spring [itex]l[/itex].

2. Relevant equations

I want to solve this using purely Newtonian methods.

3. The attempt at a solution

The position of [itex]m_1[/itex] in the center of mass frame is given by:

[tex] r_{1_{CM}} = r_1 - R_{CM} = \frac {m_2 (r_1 - r_2)}{m_1+m_2} [/tex]

Likewise, the position of [itex]m_2[/itex] in the CM frame is:

[tex] r_{2_{CM}} = r_2 - R_{CM} = \frac {m_1 (r_2 - r_1)}{m_1+m_2} [/tex]

I can write down Newton's equations for each mass using for Hooke's law [itex]r_{2_{CM}} - r_{1_{CM}} - l[/itex] as the displacement of the length of the spring from its equilibrium position.

At this point, I get two differential equations that I do not know how to solve. (Not SHM.) Can anybody help me?

Thanks.

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# Spring/Mass System with Unequal Masses

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