Oscillation and Wave

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1. If a spring with a mass m attached to it is slightly stretched or compresses with displacement x. The restoring force is given by Hooke's Law
F_r(x)= - k x ,where k is a constant
The solution to this equation is a simple harmonic oscillation.
(negligible mass of the spring).
2. Consider a spring hanging freely, stretches a length dx when it made to support a load of mass m.
The force becomes F(x) = m g - k x
The equilibrium position is x = m g / k
3. Add Damping force:
Suppose there is a viscous damping force F_b= - b v,
where b is a constant and v is the velocity of the load.
4. add external force that varies harmonically
F_ext = f_o sin( cwt )
1. w² = w_o² - (b/2m)² where w_o² = k/m, w_o is the nature frequency of the system
2. if c=0. then f_o = 0.
5. The net force acts on the mass is F = m g - k x - b v + f_o sin( cwt )

How to play?

1. You can enter values of m, k, b, f( m can also be changed with mouse click on +/- button)

b=0., f=0.	simple harmonic motion(SHM)
b!=0. (try 0.1)	damped oscillation
f!=0. (try 5.0)	forced oscillation

2. You can drag the left mouse button to change the initial position of the mass.
3. Animation starts when the mouse button is released.
4. If you drag with right mouse button ( or press ---> Button),
the spring will also move with constant speed in the horizontal direction.
5. Green arrow : the displacement x measured from the unstretched point.
6. blue arrow : the displacement x measured from the equiblibrium point (F=0).
7. red arrow : the velocity v of the mass.
8. Each time you click the mouse button, the coordinate of the mouse is shown in the textField. (MKS unit, x/v verses t )
9. External driving force:
1. c=0. means there is no external force, i.e. f_o = 0.
2. otherwise F_ext = f_o * sin ( c*w* t), where w² = k/m - (b/2m)²

URLs link to this page

1. http://www.fysik.lu.se/resurscentrum/svargym.html

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