Equilibrium of Forces on a Spring

[alexander_i]

Homework Statement

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.]

Homework 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.

The Attempt at a Solution

I first set F_net = 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.

 

[tiny-tim]

Hi alexander_i!

… 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.
…
I first set F_net = ma = -B + A/x²

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

Yes, that's the force …

but now answer the question …

what is the potential energy function?

 

[alexander_i]

Thanks for the reply!

We know dU(x) = F*dx,

and I did set up and energy equation before

E = -(1/2)*k*x² + (1/2)*m*v² - f_r*x

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

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

 

[tiny-tim]

Thanks for the reply!

We know dU(x) = F*dx …

ok, so what is U?

and what is the relation between U and K?