Write an m-file that 1. Plots f(t) over the interval o st 2 usithe equation 6)-1

Question

Write an m-file that 1. Plots f(t) over the interval o st 2 usithe equation 6)-1/2 ts ee 2. Write a MATLAB fumction find fN that determines f() gven an integer value of n and the time vector from part (1). The syntax for the calling the function must be fn = find.fa(t,N): Realize the function using a For-Loop 3. Using the MATLAB function find.IN, determine vectors representing fi(t), Jio(t), and fioo(t), and plot these functions in the figure containing flt) using a dotted, dash-dotted, and solid curve, respectively. Use a legend to distinguish the four curves in the figure, and appropriately label the axes and title the plot.

Explanation / Answer

answer to 1:

clc
clear all

t=0:1/10000:2; %% the time axis is divided into 10000 equally spaced points
F_t=t./2; %% F is calculated for each point

%% curve is plotted between F and t
hold on

title('Plot of F(t)=t/2 versus time') %% title for the graph

xlabel('time');%% x axis labeling
ylabel('F(t)=t/2');%% y axis labeling

plot (t,F_t,'k--') %% k=black -- for dashed line and the plot command

solution to 2:

function x= find_fn(t,N) %% function definition

row=1;

%% a column matrix is formed here containing the elements of the func at each time step

for time_vect=0:1/t:2
func(row,:)=time_vect./2;
row=row+1;
end

%% the value at Nth time step is returned
x=func(N,:);

solution to 3:

clc
clear all

t=0:1/10000:2; %% the time axis is divided into 10000 equally spaced points
F_t=t./2; %% F is calculated for each point

% curve is plotted between F and t

title('Plot of F(t)=t/2 versus time') %% title for the graph

xlabel('time');%% x axis labeling
ylabel('F(t)=t/2');%% y axis labeling
axis ([0 2 0 2])
hold on
plot (t,F_t,'k--') %% k=black -- for dashed line and the plot command

% these points are selected because if we divide 0-2 by 10000 points and
% want to plot that point on a scale of 1 then that value is too small to
% be visible that is why these points are taken
N1=2500/10000; %2500 point
N10=5000/10000; %5000 point
N100=10000/10000; %10000 point

% plot a curve between two point (x1,y1) and (x2,y2) as plot([x1 x2],[y1 y2])
plot([N1 N1],[0 F_t(2500)],'b:')

plot([N10 N10],[0 F_t(5000)],'g-.')

plot([N100 N100],[0 F_t(10000)],'m-')

hold off

legend('main plot','N2500','N5000','N10000')

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