Recent content by BartlebyS

but surely, for example ω=1 for the input u(t) = sin(ωt) x(t) = (1/ω)(1-cos(wt)) = 1/ω - cos(wt) = 1 - cos(t) That is a cosine not oscillating around zero like the input, but around 1. Shifted up. It will oscillate around 1 for all t. If say ω = 0.1, x(t) = 10 - cos(t), that results in...

Amazing, thankyou. I see I should have put 1/s on the third line. Is there anyway you could explain intuitively where that extra component of (1/ω) comes from? My math is bad, but I get the answer, i just don't get it! I suppose I am trying to think of the system physically adding up...

u(t) = sin(ωt) transforms to U(s) = \frac{ω}{s^{2}+ω^{2}} = \frac{1}{2j}[\frac{1}{s-jω}-\frac{1}{s+jω}] = \frac{ω}{(s+jω)(s-jω)} G(s) = \frac{1}{s} X(s) = G(s)U(s) = \frac{s}{s}\frac{ω}{(s+jω)(s-jω)} From partial fractions X(s) = A\frac{1}{s}+B\frac{1}{s-jω}+C\frac{1}{s+jω} A = sX(s)|_{s=0}...

Sorry, when I said harmonic I meant simply an oscillating input. My system is a simple one, no feedback. X(s) = G(s)U(s) where X(s) is the output, G(s) is the system transfer function and U(s) is the input. The block diagram would be U(s)------>[G(s)]-------->X(s) input...

Homework Statement In my notes it is stated that an integrator adds a phase lag of -Pi/2 and thus can cause instability. I want to understand what this really means and am deviating from the notes somewhat so do not know if I am barking up the wrong tree. Homework Equations Given a...

Thanks again mate, I played with it some more, got the answers I wanted and have a much better understanding of signal flow graphs and masons formula.

Thanks for pointing that out, so I came to the idea that a*dh/dt = dv/dt = q_in(t) - q_out(t) = 0 for steady state which would make the rest of the derivation ok I hope? Which then gave me a different drawing for the block diagram. Which gives me a loop gain of (c_1 - c_2)/as...

Homework Statement Here is the system I am looking at Homework Equations So I worked out a formula for the steady state error and put it in a form similar to masons gain formula The Attempt at a Solution But when I try and draw a block diagram and work out e I get...