# Graphing potential & kinetic energy of an oscillating particle

Graphing potential & kinetic energy of an oscillating particle!!!!

1. A particle oscillates back and forth in a frictionless bowl whose height is given by h(x) = 0.22x2 where h and x are meters. (a) Show graphically how the potential and kinetic energies of the particle vary with x.

2. I completed the (b) and (c) part of the problem, but I'm not sure as to how I graph to illustrate how the potential nad kinetic energies of the particle vary with x. Any assitance would be very much appreciated!

3. I really don't even know where to start or how to start, and how I would label my axis, etc. So if anybody can lead me in the right direction, that would be really great, becuase I'm lost!

I know that the particle has maximum kinetic energy at the bottom of the bowl in which h=0 and x=0 and that IF the maximum speed of the particle was 0.4ms-1, x=0.19 and -0.19 and h=0.008. Will this information help me in drawing the graph? Because this is what I had to determine for parts (b) and (c): "(b) Where does the particle have maximum kinetic energy? (c) If the maximum speed of the particle is 0.4 ms-1, find the x-coordinates at which the particle has maximum potential energy"

And I also know that U = mgh and if you had an h(x), you can graph U(x)...but how? That I don't know! So please please please lend your assitance!!!

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h(x) = 0.22x2 (where x2 = x squared)
As x increases in the postive and negative direction, h increases exponentially. For instance, here is a small table I constructed:
x h
-10 22
-5 5.5
-3 1.98
0 0
3 1.98
5 5.5
10 22
*If plotted, it would look like a parabola

Put the x axis, well, x, and the y axis, the energy (J).

U know potential energy is: W_p(x) = mgh(x)=mg.0.22x^2
Draw that graph, it's a parabola :D

The sum of potential and kinetic energy is constant (I call it W), u should be able to find W using the information about the max speed. Then kinetic energy is:

W_k(x) = W - W_p(x).

Now it's even easier to draw the graph of W_k(x). It's the reflection of the graph of the W_p(x) through a horizontal line.

Do some math to find some special point.