I have a transfer function that is Gs 3s48s330s248s36 After

I have a transfer function that is G(s) = 3/s⁴+8s³+30s²+48s+36. After finding the coefficients through partial fraction expansion and converting it back into the time domain I get f(t)=0.08 + 2(0.019)e^-2.8t * cos(2.5t+1.039) + 2(0.100)e^-1.2t * cos(1.1t-1.264). Now when I graph the transfer function and then graph the time domain function I get two different functions. However if i subtract the cosine funtions like this f(t)=0.08 - 2(0.019)e^-2.8t * cos(2.5t+1.039) - 2(0.100)e^-1.2t * cos(1.1t-1.264). I get the correct graph on the time domain when comparing it to the transfer function. So my question is why would I subtract the cosine functions instead of add them? Using a laplace table it showed that I would need to add the cosine functions not subtract. Any help would be greatly appreciated.

Solution

Actually we need to add the exponential terms but not subtraction. You may get nearly right answer by subtraction but not correct. Because here exponential terms are transient terms and will die with in 5 time constants. So will not play much role in the output in steady state.