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Old Nov 4th 2014, 08:13 AM   #1
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Question Oscillation problem

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 ?
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Old Nov 4th 2014, 10:43 AM   #2
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Originally Posted by MishkaMN View Post
and since
-ω2*x=(d^2*x)/dt^2 is the formula of the harmonic oscillation :
we find ω=12*pi/m
You mean ω^2=12*pi/m

Originally Posted by MishkaMN View Post
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
I would leave it as F=-4 sin(3*pi*x), and perform the integral:

W(x) = -PE(x) = integral from s=0 to s=x of 4*sin(3*pi*s)ds

Last edited by ChipB; Nov 4th 2014 at 10:46 AM.
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Old Nov 4th 2014, 10:44 PM   #3
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Originally Posted by ChipB View Post
You mean ω^2=12*pi/m



I would leave it as F=-4 sin(3*pi*x), and perform the integral:

W(x) = -PE(x) = integral from s=0 to s=x of 4*sin(3*pi*s)ds
Thank you for your reply

yeah it was w^2 sorry didnt see that

But the work done by the force is divided into not only potential energy but also kinetik energy right ?
where is the kinetik energy ?

Last edited by MishkaMN; Nov 4th 2014 at 10:51 PM.
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Old Nov 5th 2014, 01:01 AM   #4
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If by short oscillation, they mean a small value of x then sinx = x and you can approximate the oscillation as simple harmonic as Fx = - 4*pi*x. In this case 4pi = omega^2 and the rest follows. In S.H.M. the total energy is a sum of kinetic and potential, so max P.E. at the ends (when most work is done) and zero K.E. At the centre P.E. = 0 since x = 0 and K.E. is maximum.
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Old Nov 5th 2014, 04:54 AM   #5
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Originally Posted by MishkaMN View Post
But the work done by the force is divided into not only potential energy but also kinetik energy right ? where is the kinetik energy ?
If you apply force F per the given equation the spring will compress to position 'x', and at that point it has velocity =0, and consequently KE=0.
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Old Nov 11th 2014, 02:20 AM   #6
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What are oscillations and types of oscillations?

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