Math Help - Mass-Spring System

1. Mass-Spring System

Why in the mass-spring system the external force is equal to:
$F_{ext} = F_o cos( \omega t)$

What is each term of the equation?

Another question:
The mass-spring system with free vibrations are external force? And with vibration damped?

2. Originally Posted by Apprentice123
Why in the mass-spring system the external force is equal to:
$F_{ext} = F_o cos( \omega t)$

What is each term of the equation?
mass*acceleration= total force.
mass*acceleration is $m\frac{dv}{dt}= m\frac{d^2x}{dt^2}$
The spring force is -kx and you are given $F_{ext} = F_o cos( \omega t)$ so t he total force is $-kx+ F_o cos( \omega t)$.

Another question:
The mass-spring system with free vibrations are external force?
Sorry, I dont understand this question.

And with vibration damped?
Just add a damping term to the equation. Is the damping proportional to x or to v= dx/dt?