To learn about cyclical behavior of higher order systems, a physical analogy is useful because we can observe behavior over a much shorter time interval than evolving social problems. Another benefit is that the laws of physics are well established and we are not distracted by matters that are hard to agree on. Still, a spring system may not seem to be a relevant example in a course on the dynamics of social systems. However, a spring system is a stepping stone to understand social systems. Also, for social scientist to take the lead in interdisciplinary studies of social problems, they must be able to incorporate knowledge from physics, chemistry, biology etc. As pointed out earlier, System Dynamics is well suited to invite experts from different disciplines to share their intimate knowledge of the systems they study. All fields of study make use of simulations, and simulation is hardly foreign to any expert. Modeling a spring gives you more experience in making use of expert advice regarding physics.

Also important, social scientists and decision-makers often use physical analogies to make sense of complex behaviors. The pendulum that swings back and forth is an often used analogy to explain overshooting and cyclical behavior. Since the pendulum is a nonlinear system, we use a simpler linear system to explain cyclical behavior, a spring. An advantage of this choice is also that it allows us to study the third behavior mode that linear systems are capable of producing, namely cycles.

The below figure illustrates a spring.

In this quiz you will build a model of the spring system following the P'HAPI sequence.

P: Your problem is to understand the spring analogy to cycling systems. The reference mode is a mass that is moving up and down in a nice cyclical pattern over time. Since the cycles repeat themselves, the time horizon should at least cover one cycle. In case cycles are dampened or increase in strength (amplitude) over time, several cycles should be covered by the time horizon.

H: Proposing a hypothesis for the structure that causes the cycles, you rely on established theories (or laws) in physics for the individual parts of the spring system: Newton's laws of motion of the spring mass and Hooke's law for the deformation of elastic materials (the spring). Now try to build a model of these parts as you receive more hints about the involved physical laws.