Physics Help Forum Oscillation problem

 Periodic and Circular Motion Periodic and Circular Motion Physics Help Forum

 Nov 4th 2014, 09:13 AM #1 Junior Member   Join Date: Nov 2014 Posts: 2 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 ?
Nov 4th 2014, 11:43 AM   #2
Physics Team

Join Date: Jun 2010
Location: Naperville, IL USA
Posts: 2,271
 Originally Posted by MishkaMN 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 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 11:46 AM.

Nov 4th 2014, 11:44 PM   #3
Junior Member

Join Date: Nov 2014
Posts: 2
 Originally Posted by ChipB 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

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 11:51 PM.

 Nov 5th 2014, 02:01 AM #4 Physics Team   Join Date: Feb 2009 Posts: 1,425 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.
Nov 5th 2014, 05:54 AM   #5
Physics Team

Join Date: Jun 2010
Location: Naperville, IL USA
Posts: 2,271
 Originally Posted by MishkaMN 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.

 Nov 11th 2014, 03:20 AM #6 Junior Member   Join Date: Nov 2014 Posts: 2 What are oscillations and types of oscillations? Let me give you a simple explanation of What are oscillations and types of oscillations? This will help you understand the problem. Click on the link http://bit.ly/1sywpcO For more such Physics Lesson Videos, Subscribe my YouTube Channel Click here http://bit.ly/1zPAxxG

 Thread Tools Display Modes Linear Mode

 Similar Physics Forum Discussions Thread Thread Starter Forum Replies Last Post gregade Advanced Mechanics 1 Jun 27th 2012 11:10 AM HeatherN Waves and Sound 5 Sep 6th 2010 08:08 AM Bluekitten Advanced Mechanics 1 Nov 13th 2009 12:00 AM taichi2910 Kinematics and Dynamics 2 Jun 3rd 2009 05:15 PM dsptl Advanced Mechanics 1 Nov 9th 2008 02:57 PM