Dynamic physical model with example

A dynamic physical model is a physical (hardware) model whose behaviour changes with time and is used to imitate the time behaviour of a real system. Because it has a physical form, it is built from real parts (mechanical, electrical or fluid) and observed while running. Examples: a wind tunnel with a scale aircraft, a ship model in a water tank, a flight simulator, a mechanical model of a car suspension.

Example: automobile suspension (spring-mass-damper)

The car body of mass M rests on a spring (stiffness K) and a shock absorber (damping coefficient D). A force F(t) from the road acts on the body.

      F(t)
        |
     +-----+
     |  M  |   body mass
     +-----+
     |     |
    K (spring)  D (damper)
     |     |
 ====================  road / wheel

Newton's second law gives the equation of motion, with x the displacement from equilibrium:

M x'' + D x' + K x = F(t)

Here M x'' is the inertia force, D x' the damping force and K x the spring force.

• If D^2 < 4 K M, the response is oscillatory and slowly dying out (under-damped).
• If D^2 = 4 K M, it is critically damped (fastest return without oscillation).
• If D^2 > 4 K M, it is over-damped (slow return).

Electrical analogue

The same behaviour can be reproduced by a series RLC circuit, L q'' + R q' + q/C = V(t).

Features

• The model shows real, physical behaviour, so assumptions are fewer.
• It runs in real time (or scaled time) and may be costly to build and modify.
• Parameters (D, K) can be changed to find the best design before manufacture.