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in this problem well examine the two degree of freedom system and in particular well take a look at how to set up the equations of motion so we have two masses m1 and m2 and these are writing along a frictionless surface the masses are connected to one another by a linear spring of constant k2 and mass 1 is connected to the wall with a spring of stiffness k1 put in some coordinate systems here so this will be X 1 thats 1 and this will be X 2 the first thing we need to do is Freebody diagrams of each of the masses well start off with mass number 1 the free body diagram of mass 1 looks like this if i displace it to the right by an amount X 1 I will get a force by the spring in this direction K 1 times X 1 Ill get another force here equal to K 2 times X 1 minus X 2 take a second to convince yourself thats right and then by Newtons second law since then MA which in this case is m1 x1 double dot is equal to the sum of the forces because the forces are to the left but x1 is to the ri