This example shows a bouncing ball simulation using only integrator blocks in a

QFIRE CTR-101

.

Introduction

A falling ball can be described by the equations:

Furthermore, it is necessary to define an initial position above the floor (i. e. greater than zero).

When the ball touches the floor, its speed changes due to the elasticity of the ball. This effect is described by the equation:

Where

is the rising speed after the ball touching the floor, is the Coefficient of Restitution and is the falling speed before the ball touching the floor.

Simulation

The following diagram simulates the bouncing ball.

The initial position is equal to 20m and the coefficient of restitution is 0.75.  Both integrators are using external initial conditions and the Integrator 1 is using reset input. When the signal position is less or equal to zero, the first integrator, which calcules the speed, is reset changing its initial condition to the rising speed. This change is responsible for the bouncing effect.

It is possible to use the signal from Figure 2 to reproduce a real-world signal using the Analog Output Block. In Figure 4, the diagram is edited to output the ball position to an analog output.

Figure 5 shows the bouncing ball position as a real-world signal in a real oscilloscope.