Equation 1 is an expression of Newton's Law as applied to the spring-mass-dashpot model.
The forces that act upon the mass are the applied force, the force due to the spring, and the force due to the damping element.
The applied force is given in its most general sense as a force that varies with time. The applied force is:
(1)
The force due to the spring is:
(2")
The force due to the damping is:
(3")
where the force is assumed to be viscous.
By Newton's Law, the mass experiences a force that is given by:
(4").
By substituting Equation 1", Equation 2", and Equation 3" into Equation 4" yields:
(5")
Equation 5" can be rewritten to yield Equation 1:
(1)
