Consider a physical system consisting of two masses arranged as follows. The fist mass, m1, is attached to the ceiling by a spring. The second mass, m2, is attached to the bottom of the first mass by a second spring. The springs have Hooke's constants are k1 and k2. Let g denote acceleration due to gravity. (See the figure below).

In the case of no friction, suppose that the restoring force from the spring is nonlinear, i.e., suppose that when we pull the spring a distance x, the restoring force is proportional to x^3. Do computer simulations of such a system and observe its chaotic behaviour.

Please show computer simulations and the program used. As well as talk about its chaotic behaviour.

Figure 1: A two-mass two-spring system Figure 1: A two-mass two-spring system