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This will be the spring force transmitted from 1 to 2.
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This will be the force of gravity,
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or it could be an electric force
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or any other force due to anything else;
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we are not interested.
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Now, here is the interesting manipulation we're going to perform.
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We are going to add the two things on the left-hand side
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and equate them to whatever I get on the right-hand side.
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Then, I get m1·x1 double dot
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plus m2·x2 double dot,
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and that's going to be -
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I'm going to write it in a particular way,