Laplace Transforms: Vertical Motion of a Coupled Spring System

Problem Statement

Figure 1. Coupled Spring System.

Derive the system of differential equations describing the straight-line vertical motion of the coupled spring shown in Figure 1. Use Laplace transform to solve the system when k1=k2=k3=1, m1=m2=1, and x1(0)=0, x'1(0)=-1, x2(0)=0, and x'2(0)=1.1