A mass-spring system consists of two masses connected to three springs between two walls. The first spring, with spring constant k1 = 1, connects a mass m1 = 1 to a wall on the left. Then, a spring with constant k2 = 4 connects the mass m1 to a second mass m2 = 1. Finally a spring with constant k3 = 1 connects the mass m2 to the wall on the right. Let x1(t) and x2(t) represent the displacements of the two masses from their respective equilibrium positions. The motion of the system is then described by the following second-order system of DEs.

x(t) = 5x1(t) + 4x2(t) 1

x(t) = 4x1(t)5x2(t). 2

Verify that the following functions satisfy this system:

x1(t) = c1 sin(t) + c2 cos(t) + c3 cos(3t) + c4 sin(3t) x2(t) = c1 sin(t) + c2 cos(t) c3 cos(3t) c4 sin(3t) .