hi could you answer this question asap pls, thank you

The payload of a space-shuttle-pointing control system is modelled as a pure mass suspended by a spring. The relationship between the displacement pt) and force f(t) is modelled by the following equation: M dp(t).K.p(t)=f(t) with K = 0.5, M = 500 dt? (1) W (t)p(t] .(t) y(t)=P(t), show that the state and output equations are given by: X(t)= AX(t) + Bu(t); y(t) = Cx(t) 0 17 with A= B= -0.001 = [1 0.002 Check if the system is stable, controllable and observable? (iii) A state feedback control law of the form u(t)=-[k, k.]x(t)+r(t) dp(t) or u(t)=-k.p(t)-ke +r(t) dt is to be applied to the system. Find the closed-loop characteristic equation, and then Determine what conditions ko and ka should satisfy to make the system stable. Calculate the values of kp and ka that will place the closed-loop eigenvalues at -86). The payload of a space-shuttle-pointing control system is modelled as a pure mass suspended by a spring. The relationship between the displacement pt) and force f(t) is modelled by the following equation: M dp(t).K.p(t)=f(t) with K = 0.5, M = 500 dt? (1) W (t)p(t] .(t) y(t)=P(t), show that the state and output equations are given by: X(t)= AX(t) + Bu(t); y(t) = Cx(t) 0 17 with A= B= -0.001 = [1 0.002 Check if the system is stable, controllable and observable? (iii) A state feedback control law of the form u(t)=-[k, k.]x(t)+r(t) dp(t) or u(t)=-k.p(t)-ke +r(t) dt is to be applied to the system. Find the closed-loop characteristic equation, and then Determine what conditions ko and ka should satisfy to make the system stable. Calculate the values of kp and ka that will place the closed-loop eigenvalues at -86)