We have been doing a steady-state analysis of car suspension. That is,
we have looked at what happens as a car rolls over a series of bumps, ignoring
what happens when the bouncing is just getting started after the first bump or
two.
A car designer might also be interested in what happens when a car hits a
single bump, such as a break in the pavement. We can use
transfer functions to analyze this problem also.
Let's look at what happens when a car, rolling along flat pavement, rolls onto
a ``step.'' A step is a place where the road suddenly becomes a few inches
higher, such as a curb.
The calculations that we need to do involve Laplace transforms, which you will
learn about as you continue in engineering. In order for Mathematica to perform
Laplace transform operations, you must first load the Laplace transform library
into Mathematica:
Needs["Calculus`LaplaceTransform`"]
Not all of the power ofMathematica is available to you immediately upon starting
Mathematica. Much of Mathematica's more advanced capabilities are contained in
packages, which you must explicitly load when you need them. So, for
example, if you need to do Laplace transforms, you have to ask Mathematica to load
its Laplace transform library. There are many other libraries available from
within Mathematica.
The buttons below will graph the vertical position of each kind of car as a
function of time. We assume that the car rolls over a step of height 1 at time
0. Each curve starts out at zero and stabilizes at one. This is because,
after rolling up onto the step, the car ends up higher than it was before.
Notice that the time scales are different for each plot.
Plot[InverseLaplaceTransform[boat(s)/s, s, t],
{t, 0, 20}];
Next the truck:
Plot[InverseLaplaceTransform[truck(s)/s, s, t],
{t, 0, 20}];
Last the sedan:
Plot[ InverseLaplaceTransform[sedan(s)/s, s, t],
{t, 0, 20}] ;