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Determine the voltage across the capacitor and the current through the inductor:

Using the following formulae, we can easily obtain the voltage across the capacitor and current through an inductor for time t≥0,

${{i}_{L}}(t)=-\sqrt{\frac{C}{L}}{{V}_{c0}}\sin (\frac{1}{\sqrt{LC}}t)u(t)$

${{v}_{C}}(t)={{V}_{c0}}\cos (\frac{1}{\sqrt{LC}}t)u(t)$

Where

${{V}_{co}}=1V\text{ }\therefore \text{Capacitor Initial Voltage}$

Now, let us write Matlab code to compute voltage and current:

%LC Circuit Analysis clear all;close all;clc %%Circuit Parameters L= 100e-3; %Inductance (100mH) C=10e-6; % Capacitance (10microFarad) omega_o=1/sqrt(L*C); % Angular Frequency Vco=1; % Capacitor Initial Voltage Time=0:1e-5:15e-3; % Time Sampling Vc=Vco.*cos(omega_o.*Time).*heaviside(Time); % Capacitor Voltage il=-sqrt(C/L)*Vco.*sin(omega_o.*Time).*... % Inductor Current heaviside(Time); %%Plotting Capacitor Voltage and Current subplot(211) plot(Time,Vc) xlabel('Time (s)') ylabel('Amplitude (V)') title('V_C') subplot(212) plot(Time,il) xlabel('Time (s)') ylabel('Amplitude (A)') title('i_L') %=============================================

**Results:**

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