Impulse Response and Step Response

MIT RES.18-009 Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler, Fall 2015
Instructor: Gilbert Strang

The impulse response is the solution when the force is an impulse (a delta function). This also solves a null equation (no force) with a nonzero initial condition.

License: Creative Commons BY-NC-SA

[Labroidas]

God bless you, Professor Strang, thank you so much for everything you are doing for us students and for the world!

[itzmkea]

this man is one of the best teachers/professors I have ever seen

[eefunhuang]

Well said about the relationship between impulse response and step response!

[wallacechan]

Absolutely fantastic. Thank you Professor Strang.

[iwonakozlowska]

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.

[YY]

The intrinsics of the materials must have negative real part of eigen value, otherwise the function will not goes to 1 when time goes to infinity.

[DRACOBUCIO]

14:20 the most importan question in this video (my opinion). How the impulse response and the step response are related?

[PSM]

@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

[vajk]

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?

What I wouldn't give to move your mic away by about 4 inches!

[MrAngryCucaracha]

but the formula for r(t) is not the integration of the formula for g(t). Am i making a mistake?

[debajyotichoudhuri]

I am not sure how has r(t) converged to 1 asymptotically?. The added part in r(t) seems to not be converging to if s_1, s_2>0.

[wickbron]

Is unit step response equal with step response

[SimmySimmy]

Can I get output response(particular solution) under any arbitrary excitation to the system if I know its impulse response?

[roshan]

Can someone guide me to see how to find the s1-s2 on the denominator?