solution for beginner simple as possible

For the lab, use values $R=1,L={10}^{-5}H$ and $C={10}^{-5}F.$

In this section, you will use MATLAB to solve the ODEs. Here you will use the solver ode$45.$

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, $x$ dot. 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$[0,2\mathrm{.}5{10}^{-4}]$ by calling $[t,x]=$ ode$45($@RLCdynamics,tspan, $\{$:$x_0).$ This

uses the ode$45$ solver with standard settings.

Note: Consult the MATLAB documentation for ode$45$ about how to choose the values of

tspan and initial state vector $x_0.$