1. The problem statement, all variables and given/known data Hi everybody! Two masses m1 and m2 are connected with a spring one after the other to a wall (see attached picture). The spring constants are k1 and k2. To consider here are only longitudinal oscillations and no external forces. a) Express the newtonian equations of motion, when x1 and x2 represent the deflections of the two masses. b) Calculate the eigenfrequency ωi of the coupled system for the case m1 = m2 = m and k1 = k2 = k. A possible approach is x1 = A⋅cos(ωt) and x2 = B⋅cos(ωt). An explicit isolation of the equations of oscillation is here not necessary. 2. Relevant equations spring forces, differential equations for motion 3. The attempt at a solution Okay I'm still pretty confused about such oscillations (and unfortunately differential equations as well ), but I gave it a go by trying to determine the acceleration for each mass: a) m1⋅a1 = FF1 - FF12 (see picture) ⇔ m1⋅d2x1/dt2 = -k1x1 + k2(x2 - x1) ⇔ m1⋅d2x1/dt2 + k1⋅x1 - k2⋅x2 + k2⋅x1 = 0 m2⋅a2 = FF21 (see picture) ⇔ m2⋅d2x2/dt2 = - k2(x2 - x1) ⇔ m2⋅d2x2/dt2 + k2⋅x2 - k2⋅x1 = 0 Is that correct? Am I to do anything more to those equations or is that a sufficient answer to a)? b) Here I don't really know what I should be doing... I coupled the equations from a) together and applied m1 = m2 = m and k1 = k2 = k: m⋅d2x1/dt2 + m⋅d2x2/dt2 + k⋅x1 - k⋅x2 + k⋅x1 + k⋅x2 - k⋅x1 = 0 ⇔ m⋅(d2x1/dt2 + d2x2/dt2) + k⋅x1 = 0 Then I substituted d2x1/2/dt2 with their respective second derivatives: m⋅(-A⋅ω2⋅cos(ω⋅t) - B⋅ω2⋅cos(ωt)) + k⋅(A⋅cos(ωt)) = 0 ⇔ m⋅ω2⋅(A + B) = k⋅A ⇔ ω2 = k⋅A/m⋅(A + B) ⇔ ω = √(k⋅A/m⋅(A+B)) That's something... But to be honest I have almost no idea what I am doing, I just try to progress in the direction of what the problem asks me. Does ωi mean there is a different frequency for each mass? Should I be able to substitute A and B with something else? Thank you very much for your answers, I appreciate it. Julien.