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    LaPlace Transforms and Differential Equations : Masses and Springs

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    Two objects of mass M1 and M2 are attached to the opposite ends of a spring having a spring constant K; the entire apparatus is placed on a frictionless table. The spring is stretched and then released. Using Laplace transforms to solve the differential equations show that the period is:

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    Please see the attached file.


    We start with the conventional equations of motion:
    x1 denotes the position of M1, while x2 denotes the position of M2. Obviously the force the spring applies on M1 is the same as it applies on M2 only in the opposite direction:


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    LaPlace Transforms and Differential Equations are applied to Masses and Springs. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.