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I just wrote a short paper on the subject.
When masses are combined in the natural way as in m = m_1 + m_2 they have the same velocity and thus are combined in series. During an elastic collision with a spring the masses experience the same amount of force and thus are combined in parallel as in m = 1/(1/m_1 + 1/m_2) from the perspective of the spring.
You can find the paper here:
https://sites.google.com/site/nilrehob/home/documents
/Hob
When masses are combined in the natural way as in m = m_1 + m_2 they have the same velocity and thus are combined in series. During an elastic collision with a spring the masses experience the same amount of force and thus are combined in parallel as in m = 1/(1/m_1 + 1/m_2) from the perspective of the spring.
You can find the paper here:
https://sites.google.com/site/nilrehob/home/documents
/Hob
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