Oscillation and Wave

  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
  2. Fr(x)= - k x ,where k is a constant
    The solution to this equation is a simple harmonic oscillation.
    (negligible mass of the spring).
  3. Consider a spring hanging freely, stretches a length dx when it made to support a load of mass m.
  4. The force becomes F(x) = m g - k x
    The equilibrium position is x = m g / k
  5. Add Damping force:
  6. Suppose there is a viscous damping force Fb= - b v,
    where b is a constant and v is the velocity of the load.
  7. add external force that varies harmonically
  8. Fext = fo sin( cwt )
    1. w2 = wo2 - (b/2m)2 where wo2 = k/m, wo is the nature frequency of the system
    2. if c=0. then fo = 0.
  9. The net force acts on the mass is F = m g - k x - b v + fo 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)
  2. b=0., f=0. simple harmonic motion(SHM)
    b!=0. (try 0.1) damped oscillation
    f!=0. (try 5.0) forced oscillation
  3. You can drag the left mouse button to change the initial position of the mass.
  4. Animation starts when the mouse button is released.
  5. If you drag with right mouse button ( or press ---> Button),
  6. the spring will also move with constant speed in the horizontal direction.
  7. Green arrow : the displacement x measured from the unstretched point.
  8. blue arrow : the displacement x measured from the equilibrium point (F=0).
  9. red arrow : the velocity v of the mass.
  10. Each time you click the mouse button, the coordinate of the mouse is shown in the text Field. (MKS unit, x/v verses t )
  11. External driving force:
    1. c=0. means there is no external force, i.e. fo = 0.
    2. otherwise Fext = fo * 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

other java applets Welcome for your suggestion! Please click hwang@phy03.phy.ntnu.edu.tw
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