- 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).
- 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
*k* - 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. - add external force that varies harmonically
**F**_{ext}**= f**_{o}**sin( cwt )****w**^{2 }=**w**_{o}^{2 }**-**(b/2*m*)^{2}where**w**_{o}^{2}= k/m,**w**_{o }is the nature frequency of the system- if c=0. then f
_{o}= 0. - The net force acts on the mass is
**F =***m***g -***k***x**-*b***v + f**_{o}**sin( cwt )**

- You can enter values of
*m, k, b, f*(*m*can also be changed with mouse click on**+/-**button) - You can drag the left mouse button to change the initial position of the mass.
- Animation starts when the mouse button is released.
- If you drag with right mouse button ( or press ---> Button),
- the spring will also move with constant speed in the horizontal direction.
- Green arrow : the displacement
**x**measured from the unstretched point. - blue arrow : the displacement
**x**measured from the equilibrium point (**F=0**). - red arrow : the velocity
**v**of the mass. - Each time you click the mouse button, the coordinate of the mouse is shown in the text Field. (MKS unit,
**x**/**v**verses**t**) - External driving force:
- c=0. means there is no external force,
*i.e.***f**_{o }=0. - otherwise F
_{ext }= f_{o }* sin ( c*w* t), where w^{2}= k/m - (b/2m)^{2}

b=0., f=0. | simple harmonic motion(SHM) |

b!=0. (try 0.1) | damped oscillation |

f!=0. (try 5.0) | forced oscillation |