Trajectory y=x^4-x^2 with bounded y between 0 and h

[LagrangeEuler]

Homework Statement

For example particle performs a motion in x-y plane. In y there are walls from both side so particle can go in y direction from zero to $$h$$. I need to plot trajectory. If I got trajectory $$y=x^4-x^2$$ then
[tex]\lim_{x\to \infty}y(x)=\infty[/B]<h2>Homework Equations</h2><h2>The Attempt at a Solution</h2> <br /> If I got trajectory $$y=x^4-x^2$$ then<br /> $$\lim_{x\to \infty}y(x)=\infty$$, but because of the condition I may say that <b>$$\lim_{x\to \infty}y(x)=h$$. Maybe then $$y=h$$ is some natural horisontal asymptote?</b>[/B][/tex]

 

[Goddar]

Hi. It's hard to understand what your problem exactly is. Could you clarify it maybe by giving its original statement?
If you are asked to plot a two-dimensional trajectory parametrized by:
y = x⁴–x²,
Under the constraint: y_max= h,
Then it gives you a natural constraint on x as well, as a function of h; if you need to plot this you'll have to assign an arbitrary value to h so that you can plot something.
Now depending on this value, your plot will not always look the same but that's all you can do with the given information...