Coupled-Oscillators: Three Mass System • Analyze a linearly-coupled system of three masses • as shown in the figure. Suppose all the masses are equal and k₁ = k = k and k₂ = k3 = K. Write a system of equations of motion and use the semi- implicit Euler method to numerically solve. k1 k₂ k3 k₁ 0000 m1 -0000 m2 0000 m3 -0000 (Grad students) Solve the system analytically. Describe the normal modes of the system. • Consider the weakly-coupled case where к <<k as well as where к = k. • Create a simulation that shows the positions of the three masses (with lines connecting them as springs) as a function of time. Also plot the energies (kinetic, potential and total) as a function of time. (Grad students) Describe the normal-modes of the system?

Fig: 1