The step response r(t) is not exactly the integral of impulse response g(t) but it is the convolution of impulse response with the step function g(t)*u(t). r(t) is the same as presented in this video but under condition that C=1 , in other case we need to divide r(t) by C. By the way C=s1xs2.
@15:05 the step function r(t) is not the integral of g(t) as given above…….there is a 1/(s1s2) term missing in the denominator of r(t) and the +1 in r(t) equates to 1/(s1s2)…so what gives? ….are there some special initial conditions that are needed to obtain r(t) as given above?…we can let s1 = 1/s2 and that will give r(t) above, but this seems a bit contrived…I’m looking for a formal definition/proof….anyone? Cheers
If s1 and s2 are greater than 0, it indicates an unstable system meaning the output would increase exponentially rather than decaying to equilibrium, and of course it does not coverge to 1.
It would be if the initial conditions are set correctly. To see why that's the case, watch ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-ECslmuGlu-U.html where prof. Strang explains about step function and delta function. In fact the whole video is about properties of these two functions.
Thank you for the inspiring nice videos, it's a pleasure to listen your lectures. Is it possible that the initial condition for the step response is r(0)=1, instead of r(0)=0?
This professor explains thing little bit ahead. You should watch these videos first. www.khanacademy.org/math/differential-equations/second-order-differential-equations After watching the videos on Khan, please solve the c1 and c2 in these two equations: y(t)=c1e^(s1*t) + c2e^(s2*t) y(0)= c1e^0 + c2 e^0 y(0)=c1+c2=0 thus, c1=-c2 Same with y prime y prime = come on, you know how to take the derivative y prime(0) = c1*s1+c2*s2=1 y prime(0) = -c2*s1+c2*s2=1 (why do i changing the c1 to -c2? read the "thus, c1=-c2" :D) Now you can solve these as a high school math: -c2*s1+c2*s2=1 c2(s2-s1)=1 c2= 1/(s2-s1) c2 = -1/(s1-s2) what is c1? c2=-c1 let's plug in the c1 and c2 into the y(t)=c1e^(s1*t) + c2e^(s2*t). you will get y(t)= [e^(s1t)-e^(s2t)]/(s1-s2)
