Oscillations and inverse square law

  • Thread starter Anchit
  • Start date
  • #1
1
0

Homework Statement



A particle of mass m moves in 1 dimension along positive x direction.It is acted on by a constant force directed towards origin with magnitude B,and an inverse square law repulsive force with magnitude A/x^2.Find equilibrium position.

Homework Equations



B+A/x^2=m*a

The Attempt at a Solution



B+A/x^2=0
x=sqrt(-A/B)

Is this correct?
 

Answers and Replies

  • #2
2,788
587
No, the correct form is:
[itex]
m\ddot x=\frac{A}{x^2}-B sign(x)
[/itex]

Where [itex] sign(x)=\left\{ \begin{array}{ll} 1 & x>0 \\ 0 & x=0 \\ -1 & x<0 .\end{array} \right. [/itex]

Then you should solve for x<0 and x>0 separately. I hope the particle won't pass the origin!
 
  • #3
jbriggs444
Science Advisor
Homework Helper
2019 Award
8,909
3,644
No, the correct form is:
[itex]
m\ddot x=\frac{A}{x^2}-B sign(x)
[/itex]
Shyan's equation ignores the fact that the inverse square force also changes sign on opposite sides of the origin. If you include that fact, the sign() function can be simplified away.

Anchit's equation ignores the sign convention assumed in the problem: Both A and B are positive there. We do not want to be taking the square root of a negative number!!

Heed Shyan's advice and look for both positive and negative solutions.
 

Related Threads on Oscillations and inverse square law

  • Last Post
Replies
11
Views
1K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
0
Views
1K
  • Last Post
Replies
2
Views
7K
  • Last Post
Replies
3
Views
510
Replies
5
Views
1K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
1
Views
5K
  • Last Post
Replies
3
Views
936
  • Last Post
Replies
12
Views
2K
Top