# Mass-Spring System

• Dec 18th 2009, 07:32 AM
Apprentice123
Mass-Spring System
Why in the mass-spring system the external force is equal to:
$\displaystyle F_{ext} = F_o cos( \omega t)$

What is each term of the equation?

Another question:
The mass-spring system with free vibrations are external force? And with vibration damped?
• Dec 19th 2009, 04:46 AM
HallsofIvy
Quote:

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

What is each term of the equation?

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

Quote:

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

Quote:

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