Vectorizing involves using element-wise operations (a.k.a. array operations), e.g., .*, ./, .^, rather than matrix operations, e.g., *, /, ^, in order to operate on all elements of an array at once rather than one element at a time (e.g., in a for loop). Sometimes (e.g., multiplying an array by a scalar) it doesn't matter whether you use the element-wise operator or the matrix operator; when in doubt, use the element-wise operator.
Below, I assume L, C, R, and V are scalars:
% Ask for user input
% L = input('Enter the inductance (mH): ');
% C = input('Enter the capacitance (nF): ');
% R = input('Enter the resistance (Ohms): ');
% V = input('Enter the voltage (mV): ');
L = 1;
C = 10;
R = 100;
V = 1;
% Convert unit
L = L * 1e-3; %mH to H
C = C * 1e-9; %nF to F
V = V * 1e-3; %V to V
% Calculate resonant frequency
f0 = 1 / (2 * pi * sqrt(L * C)); % in Hz
fprintf('Resonant Frequency: %.2f Hz\n', f0);
%Define the frequency scale from 0 to 10,00,000 Hz (1 Mhz)
f = 0:1:2000000;
%Vrms equation calculation to be graphed
w = 2 * pi * f; % <- w is a vector the same size as f
Vrms = V * R ./ (sqrt(R^2 + ( w*L - 1 ./ (w * C)).^2)); % <- Vrms is a vector the same size as w (and therefore f)
%display graph
plot(f,Vrms);
%label the axis and title for graph
title('Frequency Response');
xlabel('Frequency (Hz)');
ylabel('Volts (V)');
