|Apr22-11, 06:27 PM||#1|
I have a object of mass m=5.34Kg. There is a force acting on the object F(x)=(5.0N/m[/2])*(x[/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)
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?
|Apr22-11, 07:49 PM||#2|
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.
|Apr23-11, 11:37 AM||#3|
sorry i was not sure about the way to write that
this is the expression for the force
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.
|Apr23-11, 11:41 AM||#4|
so i got x=0 and x=133.42
|equilibrium, oscillations, physics 1 dimension|
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