# Effect of external forces on a horizontal mass dampener

I am reading this paper which models the motion of a horizontal mass dampener.

They say that on adding a dampener, the equation consisting of the forces is:

$$ma = -cv -kx$$

where $$c$$ = damping constant, $$k$$ = spring constant $$x$$ = displacement from the equilibrium position,$$m$$ = mass of the block, $$a$$ = acceleration of the mass and $$v$$ = velocity of the mass

I am really interested in this concept of studying damped systems through differential equations. So, I was wondering what other external forces I could add to this equation, and examine how that force effects damping. For example, we could add the air resistance. Then,

$$ma = -cv -kx-\frac{\rho C_{D} A}{2} v^{2}$$

where ρ = the density of the air the object moves through, $$C_{D}$$ = the drag coefficient includes hard-to-measure effects, $$A$$ = the area of the object the air presses on.

What can be other forces I can play around with? Do factors such as temperature and pressure make a difference?

• The temperature and the pressure effect the density and also the height of your rocket for example. Die damper coefficient c is depending on the temperature, for example if you have oil dampers – Eli Oct 6 at 14:25