How do I plot 5e^(0.5t)sin(2*pi*t)

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% I have tried to plot 5e^(0.5t)sin(2pi*t) but my graph just show a negative exponential
% But when I compared to demos it's completely wrong
t1 = 0:10;
e = exp((0.5)*t1);
num6 = (5).*e.*sin((2)*pi*t1);
plot(t1, num6, 'c')

Accepted Answer

Les Beckham
Les Beckham on 24 Feb 2023
Edited: Les Beckham on 24 Feb 2023
t1 = 0:10;
e = exp((0.5)*t1);
num6 = (5).*e.*sin((2)*pi*t1);
plot(t1, num6, 'c')
grid on
You are plotting your exponential term multiplied by the sine of integer multiples of 2*pi which should be zero. Due to floating point precision issues, it is instead very close to zero and increasing in a negative direction. This causes your plot to look the way it does.
t1 = 0:10;
plot(t1, sin(2*pi*t1), '.')
grid on
If you add points that aren't integer multiples of 2*pi you will see the real behavior of your equation.
t1 = 0:0.01:10;
e = exp(0.5 * t1);
num6 = 5 * e .* sin(2*pi*t1);
plot(t1, num6, 'c')
grid on
  2 Comments
Monqiue Parrish
Monqiue Parrish on 24 Feb 2023
Thank you that makes more sense now.
Les Beckham
Les Beckham on 24 Feb 2023
You are quite welcome.

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More Answers (2)

Torsten
Torsten on 24 Feb 2023
Moved: Torsten on 24 Feb 2023
Note that sin(2*pi*t) = 0 for t = 0,1,2,3,...,10.
And these are the only points for t you specified.
  1 Comment
Steven Lord
Steven Lord on 24 Feb 2023
You can see this even better if you use sinpi instead of sin.
format longg
t = (0:10).';
y1 = sin(2*pi*t)
y1 = 11×1
1.0e+00 * 0 -2.44929359829471e-16 -4.89858719658941e-16 -7.34788079488412e-16 -9.79717439317883e-16 -1.22464679914735e-15 -1.46957615897682e-15 -1.71450551880629e-15 -1.95943487863577e-15 -2.20436423846524e-15
y2 = sinpi(2*t)
y2 = 11×1
0 0 0 0 0 0 0 0 0 0

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Image Analyst
Image Analyst on 24 Feb 2023
You had so few points that you were subsampling the shape away and couldn't see the oscillations. Use more data points. by using linspace. Try it this way:
t1 = linspace(0, 10, 1000);
e = exp(0.5 * t1);
num6 = 5 .* e .* sin(2 * pi * t1);
plot(t1, num6, 'c-', 'LineWidth', 2);
grid on
xlabel('t1')
ylabel('num6')
title('num6 = 5 .* e .* sin(2 * pi * t1)')

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