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?

  • $\begingroup$ 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 $\endgroup$ – Eli Oct 6 at 14:25

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