How to derive x(t) equation from energy

  • #1
1. Using V(x)= -max, in the following equation:
[tex] \int_{x_0}^x \frac{dx}{\pm \sqrt{{\frac{2}{m}\{E-V\left( x\right)\}}}}
\ [/tex] = t - t0

to get:
x = x0 + v0 + at2/2




E is total energy and V(x) is potential energy. I have tried hard integrating it in various ways but do not seem to get the required result.



I would really appreciate in help or tips in this regard.


When I use E - 0.5mv^2= V(x), the denominator becomes v and really does not help at all. If I do not do that, and use V(x) = -max that does not help either. I do not seem to be reaching the required equation in any way.
 
Last edited:

Answers and Replies

  • #2
tiny-tim
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welcome to pf!

hi cream3.14159! welcome to pf! :smile:

(try using the X2 icon just above the Reply box :wink:)
… to get:
x = x0 + v0 + at2/2

When I use E - 0.5mv^2= V(x)

(it should of course be x = x0 + v0t + at2/2)

why are you using E - 0.5mv2 ? :confused:

this is a perfectly ordinary integral of (constant - 2ax)-1/2

show us what you get :smile:
 
  • #3
Hi!

Thank you for the response. I solved it with someone's help. The mistake I was doing was to use 0.5mv2-m*a*x to replace E. However, using v0 and x0 instead of v and x in this expression works to give the desired result and also, one has to put t0 = 0.
 

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