How to find the point the graph crosses the x axis

Hello,

So I am trying to find the value when it crosses the x axis for the first time on the dammped spring graph each and label it so that I can a specific value. Any help would be very much appreciated

t = 0:0.005:5;
x = (0.3) .* exp(-3 .*t) .* cos(4 .* t) + 0.2 .*exp(-3 .* t) .* sin(4 .* t);
%% graphs part
plot(t,x)
hold on
yline(0,'LineStyle','--','Color','m')
xline(0.5397,'LineStyle','--','Color','r')
grid on
xlabel('Time/s')
ylabel('Displacement/m')

Answer 1

[Walter Roberson]

if x(1) == 0
    crossing_location = 1;
elseif x(1) < 0
    %crossing from negative to positive
    crossing_location = find(x >= 0, 1, 'first');
else
    %crossing from positive to negative
    crossing_location = find(x <= 0, 1, 'first');
end

if isempty(crossing_location)
        %no crossings!
else
        t_crossing = t(crossing_location);
        x_crossing = x(crossing_location);
end

Answer 2

[Matt J]

x = @(t) (0.3) .* exp(-3 .*t) .* cos(4 .* t) + 0.2 .*exp(-3 .* t) .* sin(4 .* t);

firstroot = fzero(x,[0,1])

%% graphs part
fplot(x,[0,5])
hold on
yline(0,'LineStyle','--','Color','m')
xline(firstroot,'LineStyle','--','Color','r')
grid on
xlabel('Time/s')
ylabel('Displacement/m')