# Homework Help: Equilibrium of Forces on a Spring

1. Jun 15, 2009

### alexander_i

1. The problem statement, all variables and given/known data

A particle of mass M moves in one dimension along the positive x axis, under the influence of two forces. The first force is a constant force, with magnitude B and direction toward the origin. The second force is an inverse square law, with magnitude A/x2 and direction away from the origin.

[Data: M = 0.30 kg; B = 14 N; A = 34 Nm2.]

2. Relevant equations

Find the potential energy function, and sketch the energy diagram for motion with kinetic energy K. Find the equilibrium position.
Calculate the frequency of small oscillations around the equilibrium.

3. The attempt at a solution

I first set Fnet = ma = -B + A/x2

1st: Am I correct to say the resorting force (toward the origin) is - ?

if so, I then rearranged the problem to look like a differential:

m*x$$^{''}$$ + B = A/x2

divide by m, and multiply by x2,

x2*x$$^{''}$$ + B*x2/m = A/m

Is the set-up correct? or do I need a velocity term in here? Thanks for any help, or criticism as to how to write my questions better.

2. Jun 16, 2009

### tiny-tim

Hi alexander_i!
Yes, that's the force …

what is the potential energy function?

3. Jun 16, 2009

### alexander_i

We know dU(x) = F*dx,

and I did set up and energy equation before

E = -(1/2)*k*x2 + (1/2)*m*v2 - fr*x

and when I take the derivative, I of course get back to my Fnet.

Am I trying to solve this differential? or did I not pick up on your question?

4. Jun 16, 2009

### tiny-tim

ok, so what is U?

and what is the relation between U and K?