- An object that is attached to a spring that is slightly stretched or compressed by a displacement x will experience a restoring force given by Hooke's Law:
Fr(x)= - k x ,where k is a constant
The solution to this equation is a simple harmonic oscillation (we assume that the mass of the spring is negligible).
- Consider mass that is attached to a spring that is hung from the ceiling:
If the spring is stetched, or compressed, by an amount x, then the force exerted on the mass is equal to F(x) = m g - k x
The equilibrium position is x = m g / k
- Damping forces:
A viscous damping force can be modeled as Fb= - b v, where b is a constant and v is the velocity of the load.
- External, harmonic forces:
- w2 = wo2 - (b/2m)2 where wo2 = k/m, wo is the nature frequency of the system
- if c=0. then fo = 0.
- The net force acts on the mass is F = m g - k x - b v + fosin(cwt)