How is the expression for V(x) plotted using singularity functions?

[princejan7]

Homework Statement

Can someone explain how the expression for V(x) is plotted?

Homework Equations

The Attempt at a Solution

I understand the plots for the dotted lines but not how they got the actual plot for V(x)

 

[CWatters]

It's been awhile since I did this but I think you just sum the dotted curves region by region.. I'll do the region shown in green on my copy of your diagram..

At the start of the region you have..

+8 from (a)
-32 from (b)
+0 from (c)
+40 from (d)
= +16

Then at the end/right you have

+8 from (a)
-48 from (b)
+16 from (c)
+ 40 from (d)
= +16

So in that region the result is a horizontal line at +16.

 

[princejan7]

It's been awhile since I did this but I think you just sum the dotted curves region by region.. I'll do the region shown in green on my copy of your diagram..

At the start of the region you have..

+8 from (a)
-32 from (b)
+0 from (c)
+40 from (d)
= +16

Then at the end/right you have

+8 from (a)
-48 from (b)
+16 from (c)
+ 40 from (d)
= +16

So in that region the result is a horizontal line at +16.

thanks, I have another question:


at x=6, I'm supposed to be getting V(x)=0 but summing the dotted curves, I get

(23/4) -3(6) +3(3) + (1/6)(6^2) - (1/6)(3^2) + 2(3) + (7/4)
=9

 

[BvU]

thanks, I have another question

Does that mean you think the exercise has been answered properly ? I think I see an ans (2) on the picture, but I have no idea what the question is!
By the way: read the guidelines and fill in the template. Include an explanation of what <> [ ] and the superscripts 0 and 1 mean. That way others can read what this is about!

You then post another question: "I'm supposed to be getting V(x)=0". Well, I get that too, but just by deciphering the funny code these authors use to indicate intervals and to describe V. Not by dallying around with 23/4 and all kinds of other fractions. What is this ? Where do you get these dashed lines from? What do they represent ?

 

[HalfLostAndSearching]

from those lines. Can someone please clarify?The expression for V(x) is plotted by using the values of x and the corresponding values of V(x) to create a graph. The dotted lines represent the values of V(x) at different points along the x-axis. To get the actual plot for V(x), these points are connected with a continuous line, creating a curve that represents the function V(x). This curve can then be analyzed and studied to understand the behavior of V(x) at different values of x. It is important to note that the plot of V(x) is just a visual representation of the function and does not necessarily show all the details or characteristics of the function. It is always important to also consider the mathematical expression for V(x) and any other relevant equations or principles when analyzing a plot. I hope this helps clarify the process of plotting singularity functions.