It probably should be a decaying sinusoid.
The problem is that it decays too fast. Decreasing the magnitude of ‘t’ helps to visualise it correctly. (I suspect the problem is the ‘exp(-t./2)’ term. The constant should be smaller than 0.5 to get the result you lilely want with the original ‘t’.)
t=linspace(0,100,101)/10;
y = 3.*exp(-t./2).*cos(4.*pi.*t);
plot(t,y);
grid
.
