The systemmodels a coupled oscillator. Imagine a spring (with spring constant k1) attached...

The system

models a coupled oscillator. Imagine a spring (with spring constant k1) attached to a hook in the ceiling. Mass m1 is attached to the spring, and a second spring (with spring constant k2) is attached to the bottom of mass m1. If a second mass, m2, is attached to the second spring, you have a coupled oscillator, where x and y represent the displacements of masses m1 and m2 from their respective equilibrium positions.

If you set x1 = x, x2 = x′, x3 = y, and x4 =y′, you can show that

Assume k1 = k2 = 2 and m1 = m2 = 1. Create an ODE file and name it couple.m. Suppose that the first mass is displaced upward two units, the second downward two units, and both masses are released from rest. Plot the position of each mass versus time.