I'm given a problem by the following:
Find the sinusoidal steady state response (in the time domain) of the following systems modeled by transfer function, P(s), to the input u(t). Use the Bode plot (in Matlab bode.m) of the frequency response as opposed to solving the convolution integral of the inverse Laplace transform.
$$ P(S) = 11.4/(s+1.4), u(t) = cos(5t) $$
I'm a bit confused by the question because I thought bode plot is the definition of steady state response, but it's asking me to find it in time domain. Is such thing possible? Anyways plotting this in matlab gives me the following:
$$ Y(S) = P(S)U(S) $$
where from laplace transform
$$ U(S) = s/(s^2+25) $$
Y =
11.4 s
-------------------------
s^3 + 1.4 s^2 + 25 s + 35
Continuous-time transfer function.
>> bode(Y), grid
This doesn't look like a typical bode plot either (Maybe because output is third order?) What can I infer from this representation of bode plot?
Edit: So this is a bode plot for just P(s)
At w = 5, it seems like the phase of -75 degrees and magnitude of 7db
Since magnitude in db, the final steady state response in time domain is
$$ Y_sss(t) = 2.24cos(5t - 75^{\circ}) $$
Really? This simple?