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

-ω2*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)) ?

then to find potential energy:

umm..., i have no other ideas other than using VIOLENCE(hihi) to solve this problem :P 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 ?