$9209\mathrm{.}505$

$7$ Figure $6$ shows a mass spring$-$damper system containing two masses $M_1$ and $M_2.$

$3$ Dee

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An external force $f(t)$ is applied on $M_2$ in the direction shown. The two masses are connected via a spring of spring constant kg and a damper of viscous friction coefficient $B_3.$ The masses $M_1$ and $M_2$ are also connected to a rigid body via two separate spring damper combinations of spring constants $k_1,B_1$ and $k_2,B_2$ respectively. The viscous iriction coefficient between the rigid body and the masses is $B_3.$

derive the transfer function from the input f$($t$)$ to the output x$1$