Find Stable Equilibrium for Mass m=5.34Kg w/ Force F(x)

[jjj2364]

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

 

[ideasrule]

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.

 

[jjj2364]

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 going to do that again and I am going to try to do part two.
thanks!
bob

 

[jjj2364]

so i got x=0 and x=133.42