ANSLOM,

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

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

m$\ddot{x}$ + c$\dot{x}$ + kx + kx = ky

m$\ddot{x}$ + c$\dot{x}$ + 2kx = ky sin wt

We know that

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

Fo = ky

Keq = 2k

$\frac{X}{X_{st}} = \frac{1}{\sqrt{(1-r^2)^2 + (2 \xi r)^2}}$

$X = \frac{ky}{\frac{2k}{\sqrt{(1-r^2)^2 + (2 \xi r)^2}}}$

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