$m\ddot{x} \ = \ - c\dot{x} \ - \ \frac{2k}{3} \ x – 3k \ (x – y)$

$m\ddot{x} \ + \ c\dot{x} \ + \ \frac{2k}{3} x \ + \ 3k (x – y) \ = \ 0$

$m\ddot{x} \ + \ c\dot{x} \ + \ \frac{2k}{3} x \ + \ 3 kx \ = \ 3ky$

$m\ddot{x} \ + \ c\dot{x} \ + \ \frac{11k}{3} \ x = 3k \ Yo \ sin \ wt$

On comparing,

m$\ddot{x}$ + c$\dot{x}$ + kx = Fo sin wt

$X_{st} \ = \ \frac{fo}{k} \ = \ \frac{3kyo}{\frac{11}{3}k} \ = \ \frac{9}{11} yo$

$X \ = \ \frac{ \frac{9}{11} yo}{\sqrt{ (1- r^2)^2 + (2 \xi r)^2}}$