Re: How do trampolines(their spings and the mat/bed) work? Please E-mail ASAP

Trampolines could be modelled as one big spring. The tricky part about bouncing on a trampoline is modelling the motion of the bouncer! Let me explain.

A system with motion is best described by the differential equations that explain the interaction of the forces as position and velocity. Instead of going into the equation, let's look at the important forces.

When someone bounces on a trampoline, there are several forces at work:

-weight of the person
-restoring force of the trampoline (the springs and nylon).
-dampening of the trampoline
-Impulse or driving force created by the jumper

A spring will follow Hooke's law Force = - Constant * displacement,
where the Constant (spring constant) depends on the spring and the minus sign indicates that the spring's force is in the opposite direction of its displacement (compressed spring pushes out, stretched spring pulls in). This is called the restoring force because it tries to return the spring to its equilibrium position.

For example, suppose you hang a weight from a spring.

s represents the unstreched spring
S represents the stretched spring



 
     s              S
     s              S
     s              S
     s              S
     s  ----------  S  -------------- unweighted spring equilibrium
position
                    S
                    S
                    S
              XXXXXXXXXXXXX
              XXXXXXXXXXXXX
              XX Weight  XX
              XXXXXXXXXXXXX
              XXXXXXXXXXXXX

The balance of forces for a static system:

Weight + Force of spring = 0 (This is a vector equation)

If I choose the upward direction as positive:

-mg + kx = 0.

A spring will oscillate if a force (or weight) is added of changed quickly. The oscillation has a frequency that is dependent on the spring constant and the mass of the thing attached to the spring. The object will continue to oscillate forever unless a dampening force is present to remove energy. Here, quickly could be loosely interpreted as faster than the dampening of the spring system. The dampening is the force that causes the spring to eventually stop oscillating.

In addition to this, the person creates impulses (short bursts of force or momentum imbalance) by jumping, bouncing, changing position, etc. This is referred to as a driving force. The jumper jumps against the trampoline, the trampoline is displaced from equilibrium and pushes back against the jumper. If the jumper works out the timing properly, the trampoline will add energy to the jumper's leap creating a big bounce!!! Similarly the jumper can absorb the spring of the trampoline to eventually come to rest once again.

There are some wonderful Java applets on the web that show the interactions of dampening, spring constant, and mass of the object attached to the spring.

References and further investigation

guelph tutorial

java

spring

manitoba interactive

Sincerely,

Tom "Spring Loaded" Cull