How to work out the noise power and SNR in the systems output?

I have this 2nd order underdamped system with the following equation:

damp = 0.15;
natural_freq = 5;

theta = acos(damp);
wd = natural_freq*sqrt(1-damp^2);

t = 0:0.0251:6
% fitted model
y =  1 - (1/sqrt(1-damp^2))*exp(-damp*natural_freq*t).*sin(wd*t + theta);

How do you obtain an estimate of the noise power as well as signal-to-noise ratio (dB) present at the system’s output.