Graph the potential of an anharmonic oscillator

Click For Summary
SUMMARY

The discussion focuses on graphing the potential of an anharmonic oscillator using the potential energy equation U(x) = 1/2 kx². The user expresses difficulty in determining the spring constant "k" and the appropriate x-axis values for plotting. They clarify that the potential U(x) can be derived from the integral of the force F, where F is defined as F = ma = m d²x/dt². This integral approach provides a comprehensive method for calculating and graphing U(x) across a specified range of x values.

PREREQUISITES
  • Understanding of potential energy equations in physics
  • Familiarity with force equations, specifically F = ma
  • Basic calculus for integration
  • Experience with graphing functions in a spreadsheet tool
NEXT STEPS
  • Research how to determine the spring constant "k" for different systems
  • Learn about integrating force to find potential energy in various contexts
  • Explore graphing techniques for plotting potential energy functions
  • Study anharmonic oscillators and their characteristics compared to harmonic oscillators
USEFUL FOR

Students studying classical mechanics, physics educators, and anyone interested in understanding the dynamics of anharmonic oscillators and potential energy calculations.

curto
Messages
19
Reaction score
0

Homework Statement



my spreadsheet: (oh and please ignore the fact that I've got my amplitude set to 39, i was still answering question 1 when i took the screen shot)

Untitled-1-1.png


the question i am currently having problems with is question 2:

Untitled-2-1.png


Homework Equations



i know the potential is U(x) = 1/2kx2 but that's about all i know

The Attempt at a Solution



i would use the above equation to find U which would be plotted on the y axis, however i don't know what the constant "k" is. also i don't know what i would use as the x axis
 
Physics news on Phys.org
i figured it out but just for anyone else who would like to know, its actually quite simple. the potential U(x) is equal to the integral of -F dx. simply find an expression for F (remember F = ma = m d^2x/dt^2) and then integrate. that's going to be your expression for U(x). then all you got to do is plot U(x) where x can have any range.
 

Similar threads

  • · Replies 10 ·
Replies
10
Views
2K
Replies
13
Views
2K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 14 ·
Replies
14
Views
3K
  • · Replies 5 ·
Replies
5
Views
2K
Replies
9
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
Replies
1
Views
3K
Replies
3
Views
843