## stable equilibrium

I have a object of mass m=5.34Kg. There is a force acting on the object F(x)=(5.0N/m[1][/2])*(x[1][/2])-(1.0N/m)*(x).
1)I need to find the position x0 where the mass is in a condition of stable equilibrium.
2)What is the frequency of oscillation around this position? How would this frequency change if the force was F(x)=(1.0N/m)(x)

Relevant equations:
F(x)=0 in order to get the position of stable equilibrium.

The attempt at a solution
I put the force F(x)=0 and I got x=0 and x=25 but I'm not sure this is the right way to do it.
For part 2 I'm a little confused, could give some hints?

thanks
jon

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Recognitions:
Homework Help
 I put the force F(x)=0 and I got x=0 and x=25 but I'm not sure this is the right way to do it. For part 2 I'm a little confused, could give some hints?
That's the right way to do it, but I can't check your answer because I don't understand your notation. What do m[1][/2] and x[1][/2] mean?

For part 2, think about the differential equation for a harmonic oscillator:

d2s/dt2 + w2s=0

where s represents a small deviation from the equilibrium position. Try taking the second time derivative of x, then rewriting it in the form above, using Taylor series approximations if necessary. w^2 would then give you the frequency.

 ok sorry i was not sure about the way to write that this is the expression for the force F(x)=(5.0N/m^1/2)*(x^1/2)-(1.0N/m)x m=mass so the first term contains the sqrt of m and the sqrt of x. I think i made a mistake in the calculation because i didi not plug in the value for the mass. I'm gonna do that again and im gonna try to do part two. thanks! bob

## stable equilibrium

so i got x=0 and x=133.42

 Tags equilibrium, oscillations, physics 1 dimension