 
Summary: 5. DYNAMICS OF COUPLED MASSES 19
5 Dynamics of coupled masses
The purpose of this exercise is to study some interesting oscillatory phenomena. Consider the
following massspring system:
MM
w1
k1 k2
w2
k1
We assume that there is no influence by gravitational or frictional forces. The two masses are
taken to be unity. When both masses are in their respective equilibrium positions, the three
springs are neither compressed nor stretched. The variables w1 and w2 are the displacements
from the equilibrium position of the masses.
Tasks
1. Using Newton's second law, that is the sum of the forces = mass × acceleration ( F = m×a
), derive the force balance for both masses.
2. Rewrite the two force balances to dw
dt = Aw, with w = [w1, dw1
dt , w2, dw2
dt ]T
