Question

A spring with constant k1 is attached vertically to the ceiling and a sphere of mass m1 hangs from the other end of the spring. Another spring, this one with constant k2 is attached vertically to the first sphere. Finally a second sphere (mass m2) is attached to the lower end of the second spring. Assuming that the spheres can only move vertically and using y1 and y2 as coordinates measured from the equilibrium position of each sphere, show that the equations of motion can be expressed as M ¨~y = −K~y where ~y = y1 y2 , and M and K are 2 × 2 matrices. Find those matrices as well

Answer 1