B$.$ Simulating the RLC circuit in MATLAB $(30\%$;$25\%)$

In this section, you will use MATLAB to solve the ODEs you derived in Section A$.$ Matlab supports many different numerical

schemes for solving ODEs. Here you will use the solver ode$45,$ which is based on a variable step Runge$-$Kutta method.

Assume $R=2,L={10}^{-3}H$ and $C={10}^{-3}F.$ Choosing as states $x_1=$i and $x_2=v_C,$ write a MATLAB function

xdot $=$ RLCdynamics $(t,x)$ that takes as inputs the time $t$ and the vector of states $x,$ and returns the vector of

time$-$derivatives of the state, xdot. Assume a constant input voltage of $v(t)=1V.$ You may hard$-$code the values for

$R,L$ and $C$ given above or$,$ alternatively, use global variables. Note: Your derivatives will not explicitly depend on the

time $t.$ The reason the function RLCdynamics takes $t$ as an argument is that MATLAB's ODE solvers expect this

particular form.

Solve the system of ODEs numerically for the initial condition $i(0)=v_C(0)=0$ on the time interval tin$[0,4*{10}^{-2}]$ by

calling $[t,x]=$ ode $45($@RLCdynamics,tspan,$x0).$ This uses the ode $45$ solver with standard settings. Consult

the MATLAB documentation for ode $45$ about how to choose the values of tspan and initial state vector $x0.$

Plot the evolution of the current i and the capacitor voltage $v_C$ as a function of time in a single plot.