JUST DO $6\mathrm{.}2!!!$

$6\mathrm{.}1$ Figure P$6\mathrm{.}1$ shows a flywheel with moment of inertia $J=0\mathrm{.}5kg-m^2$ that is initially rotating at an angular velocity ${}_0^{}=40ra\frac{d}{s}.$ The flywheel is subjected to friction, which is modeled by linear viscous frictiontorque $b{}^{},$ with friction coefficient $b=0\mathrm{.}06N-m-\frac{s}{r}ad.$ Use Simulink to obtain the dynamic response and plot the angular position $(t)($in rad$)$ and angular velocity ${}^{}(t)($in $ra\frac{d}{s}).$ In addition, use the simulation to integrate the rate of energy dissipation ${}^{}$ and plot dissipated energy $($in J $)$ versus time. Show that the total dissipated energy as computed by the simulation is equal to the system's initial energy.

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Figure P$6.1$

$6\mathrm{.}2$ Repeat Problem $6\mathrm{.}1$ with the addition of dry $($Coulomb$)$ friction torque, $T_{\text{d}\text{r}\text{y}}sgn({}^{}),$ where $T_{\text{d}\text{r}\text{y}}=0\mathrm{.}1N-m.$ Linear viscous friction torque $(b=0\mathrm{.}06N-m-\frac{s}{r}ad)$ also acts on the flywheel.