Write different equation from physical system

[Maurizio]

Hi to all,

I've to write differential equation for desciribe system in attached file.

The system is intended: from force f as input to position x2 as output.

Initial condition are the following x1=0 and x2=0.

In the attached file I've included all formula for descrive relationship between force and position for components: Spring, suspension.

I'd like some suggestion about ho to resolve this kind of problem.

I've found result for this exercise, I've try to computate the valur, but I made samo mistake, cold you suggest if my starting equation are correct, if they're not could you explain my where I made error?

Starting Equation:
f + k(x1-x2) + BD(x1-x2)=D^2mx1
-k(x1-x2)-BD(x1-x2)=D^2mx2

Expand First and Second Equation
f +kx1 -kx2 +BDx1 -BDx2 = D^2mx1
-kx1 +kx2 -BDx1 +BDx2 = D^2mx2

Aggregate for common factor x1
( k + BD - D^2m )*x1 = -f + kx2 +BDx2
( -k -BD )*x1 = -kx2 -BDx2 +D^2mx2

Computate x1
x1 = ( -kx2 -BDx2 +D^2mx2 ) / ( -k -BD )

Replace x1 in first equation:
( k + BD - D^2m )*( -kx2 -BDx2 +D^2mx2 ) / ( -k -BD ) = -f + kx2 +BDx2

( k + BD - D^2m )*( -kx2 -BDx2 +D^2mx2 ) = (-f + kx2 +BDx2) * ( -k -BD )

-k^2x2 -kBDx2 + kD^2mx2 -BDkx2 -B^2D^2x2 +BD^3mx2 +kD^2mx2 + BD^3x2m D^4m^2x2
= +kf -fBD -k^2x2 -kBDx2 -kBDx2 -B^2D^2x2

+kD^2mx2 +BD^3mx2 +kD^2mx2 + BD^3x2m -D^4m^2x2
+kf -fBD

My result:
-D^4m^2x2 + BD^3x2m + BD^3mx2 +kD^2mx2 +kD^2mx2 = +kf -fBD

Correct Result:
+D^4m^2x2 + BD^3x2m + BD^3mx2 +kD^2mx2 +kD^2mx2 = +kf +fBD

Thank you very much!

Bye
Maurizio

 

[NSAC]

Replace x1 in first equation:
( k + BD - D^2m )*( -kx2 -BDx2 +D^2mx2 ) / ( -k -BD ) = -f + kx2 +BDx2

( k + BD - D^2m )*( -kx2 -BDx2 +D^2mx2 ) = (-f + kx2 +BDx2) * ( -k -BD )

-k^2x2 -kBDx2 + kD^2mx2 -BDkx2 -B^2D^2x2 +BD^3mx2 +kD^2mx2 + BD^3x2m D^4m^2x2
= +kf -fBD -k^2x2 -kBDx2 -kBDx2 -B^2D^2x2

Your mistake is in the multiplication (-f + kx2 +BDx2) * ( -k -BD ). On the right hand side rather than -fBD you should get +fBD