Homework Help: Oscillation problem

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1. Oct 31, 2014

Misheel

1. The problem statement, all variables and given/known data
mass "m" object is located near the origin of the coordinate system. External force was exerted on the object depending on the coordinate by the formula of Fx=-4*sin(3*pi*x). Find the short oscillation period, and the potential energy depending on the coordinate.

2. Relevant equations
F=ma

3. The attempt at a solution
I am not really sure what is the short oscillation period... but
since there is only 1 force:
F=Fx=ma
-4sin(3*pi*x)=m*(d^2*x)/dt^2

and assuming that the object will move very little (because it's said to be SHORT osccilation period ?)
sin(3*pi*x) is approximately 3*pi*x .
and since
2*x=(d^2*x)/dt^2 is the formula of the harmonic oscillation :
we find ω=12*pi/m
and the T=2*pi*√(m/(12*pi)) ?

and also assuming that in SHORT oscillation :
it is almost like a spring :
F=-12*pi*x=-kx
k=12*pi

potential energy is Ep= k*x^2/2=6*pi*x^2 ???

2. Oct 31, 2014

vela

Staff Emeritus
This is fine.

I think the problem is looking for the potential corresponding to the original force, not the approximation.

3. Oct 31, 2014

Misheel

Thank You for your reply, Vela

umm...then, i have no other ideas other than using FORCE to solve this problem :PP which is :
F=-kx
Fx=F=-4*sin(3*pi*x)=-kx from this
we find k=4*sin(3*pi*x)/x
so Ep=kx^2/2=2*sin(3*pi*x)*x ???

is it right ? :P

Thanks

4. Oct 31, 2014

vela

Staff Emeritus
How are potential energy and force related in general?

5. Oct 31, 2014

Misheel

Maybe the work done by force is divided into object's konetik and potential energy ?

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