Sinusoidal response to sinusoidal input (Process control)

[guiromero]

Homework Statement

The sinusoidal response is a common response type in first-order industrial process control systems. This response is characterized by the oscillation that occurs in the controlled variable around its steady state value, when a sinusoidal input is applied to the system. Which of the following correctly describes one of the main characteristics of the sinusoidal response in first-order systems?


a) The amplitude of the sinusoidal response is not affected by the frequency of the sinusoidal input.
b) The amplitude of the sinusoidal response increases as the frequency of the sinusoidal input increases.
c) The amplitude of the sinusoidal response decreases as the frequency of the sinusoidal input increases.
d) The phase of the sinusoidal response is directly proportional to the frequency of the sinusoidal input.
e )The phase of the sinusoidal response is inversely proportional to the frequency of the sinusoidal input.

Relevant Equations

G(s) = K/(Ts + 1) (basic first orde transfer function)

This a homeawork from my graduate course. I know that a sinusoidal input affects both the amplitude and phase of the response, but I don't know how it does.

I'd be really glad if someone could help.

Thanks

 

[FactChecker]

It might help to be a little more precise in the statements. If you mean 1/(Ts+1), then write that, not 1/Ts +1. If you mean first order LAG, then write that. If you mean amplitude GAIN, then write that. If you mean phase SHIFT, then right that.
That being said, how do you think that a first order lag would respond to faster frequencies? A lag is slow to respond. That should help you to rule out a lot of the incorrect answers.
We can not give answers to homework-type problems and can only give guidance and hints for your work. So I don't think that I can say more.

 

[guiromero]

That was great! Thanks a lot!