Parameter Identification for $2$nd

order System

We consider a mass$-$spring$-$damper system with force $F(s)(N)$ as input and displacement $x(s)$

$(m)$ as output, which has the transfer function as:

$G(s)=\frac{x(s)}{F(s)}=\frac{1}{M{s}^2+bs+K}$

where $M,b$ and $K$ are mass, damping coefficient and stiffness, respectively. The plot below is the

step response of the system under step input with amplitude of $1$ N $.$

$1-$Find the static gain of the system. $(3$ points$)$

$2-$Find the damping ratio based on $OS\%.(6$ points$)$

$3-$Find the undamped natural frequency of the system with the oscillation period and the

damping ratio found in step $2).(4$ points$)$

$4-$Referred to the transfer function given above, please find out the values of $M,b$ and $K$ based

on your results in Parts $1,2$ and $3.(6$ points$)$