Total Response Example #1 (Part 1/2)

The total response y(t) of a linear system can be written as the sum of its zero-input response and zero-state response, where the zero-state response is computed via the convolution integral.

We solve for the total response of a system described a differential equation with initial conditions. This "lengthy" problem involves the following steps:

1) Compute the zero-input response y0(t)
2) Compute the impulse response h(t)
3) Compute the zero-state response yzs(t) = h(t) * f(t) where "*" is the convolution operator.
4) Compute the total response y(t) = y0(t) + yzs(t)

We work the first 2 parts of this process in this video, the remaining parts are work in Part 2/2.

[kyrinky]

This example is wild. Everything from last semester's course of linear systems just came back to mind. Thanks Adam, you saved me then, and now again.

[MrPbballer]

you're an absolute legend! after 2 hours of searching, I find your video that gives a brilliant example.

[acedelgado]

Thank you so much for your videos, every resource either makes things extremely complicated or only does theory.
Thank you

[jason-]

Thank you kind sir that you passed your knowledge in such simple way.

[jackharrison]

This might be a shot in the dark, but how come @6:50 you multiply the second part of the derivative by 2, (so the 2( 1 - e^(-t)) part?) I'm super confused on why you double it, is it because of the lone number in ( D + 2 ) which is 2? Thank you so much!

[MrHjld]

Why is there a unit step response part at 3:21? Where does this come from? Is it because the function is only defined at t>0 ?

[sagarreddy]

while computing impulse response. how to determine the value of bn when nis equal on both sides.

[DirtyPhlegm]

Why. Are. There. So. Many. Freaking. LETTERS!?