$7\mathrm{.}34$ An engineer wants to develop a model of an existing mechanical system that has complicated geometry.

She suspects that a low$-$order linear model may provide an accurate representation of the complex system.

She applies a step torque input T$\_($in $)($t$)=0\mathrm{.}6$U$($t$)$N$-$m and measures the angular position of the rotational

system. Figure P$7\mathrm{.}34$ shows the step response she obtains by experimentation.

Figure P$7\mathrm{.}34$

a$.$ Develop a transfer function for the mechanical system.

b$.$ Use MATLAB or Simulink to simulate the step response of the transfer function developed in part

$($a$)$ using the torque input T$\_($in $)($t$)=0\mathrm{.}6$U$($t$)$N$-$m$.$ Compare the simulation result to Fig. P$7\mathrm{.}34.$ Is the

low$-$order linear model accurate?