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Thanks for your replies but I have another question I want to find the equation of damper ratio ζ>1 but including cubic spring I know that for linear active (non cubic ) suspension is ζ= (c√m)/(2m√k) but in my case that i have cubic spring do you have any idea how the equation is

Yes

δ is just a symbol δ = ( z-1 )^3 nit derivative And my problem says that F spring = - kδ^3(t) I dont know how to turn u it to x dot

ma= F(t) - mg - Fspring -Fdamper

i am trying to make these x dot dot ,x dot etc but there is δ^3(t) i dont how to make it to x

F(t) up force F spring , F damper and weight down force

Hello So I need to solve a problem on an active suspension .I dont know how to find the equations of state space on open loop Given information We apply F(t) force as ypou can see z(t) is the distance of the upper spring edge from the ground when spring length (not loaded ) = 1 F...