Calculating steady state response to periodic force input (mass spring damper system)

I am trying to calculate the steady state response for the system defined in my code below to a periodic force of cos(t) using fft.

if true
  % code
end
m=4;               
k=256;                 
c=1;
wn=sqrt(k/m);
z=c/2/sqrt(m*k);
wd=wn*sqrt(1-z^2);
w=sqrt(4*k*m-c^2)/(2*m);
x0=0;
v0=0;
%%%%%%%%%%%%%%%%%%%%%%%%%
n=100;
t=0:1/n:2*pi;
f=cos(t);
F=fft(f);
h=1/m/wd*exp(-z*wn*t).*sin(wd*t);
H=fft(h);
conv=H.*F;
plot(t,ifft(conv))

HERE is the numerical solution using RK4 method. You can see the system reaches a steady state response to the cos(t) input force.

 I expect to see that steady state response using this fft method above but what i get is the following:

The amplitude is way off, so i know i am doing something wrong.

(My goal is to use FFT function to get the periodic steady state response)

So what am i doing wrong? How can i properly use fft to find the solution? and how can i plot the solution for more than one period without changing the t vector? When i change the max t from 2*pi to lets say... 10*pi, it changes the plot to a greater amplitude! Why is this?! Do i have to perform the convolution over 1 period (0:1/N:2*pi) or does this not matter at all? Are there benefits to increasing this range, or does it matter since the Fourier transform assumes periodic input? I am pretty confused and uneducated on this topic, so help would be appreciated!