Question

Basic Engineering Circuit Analysis (11th Edition) Chapter 13, Problem 4P 口 RA Bookmark Show all steps: ON Problem Use property number 7 to find t0)] if t) te- at u(t-1).

Can someone please solve this problem? I see that it is already solved online but I would like to see a second solution to it. Please show how property 7 is used to solve this. Thank you.

Answer 1

E^at sin b t = b/(s - a)^2 + b^2: s > a e^at cos b t = (s - a)/(s - a)^2 + b^2: s > a another property e^at sin b t u(t - c) = b e^-c s/(s - a)^2 + b^2 e^a t cos b t u(t - c) = (s - a) e^-c s /(s - a)^2 + b^2 t^n x(t) = (-1_)^n d^n/d s^n [x(s)] given f(t) = t e^- at u (t - 1) taking laplace on both sides f(s) = (-1)^n d/ds{L[e^-at u(t - 1)]} = -1 d/ds{e^-s/(s + a)} f(s) = -[(s + a)e^-s (-1) - e^-s /(s + a)^2] f(s) = (s + a)e^-s + e^-s/(s + a)^2 f(s) = (s + a)e^-s/(s + a)^2 + e^-s/(s + a)^2 f(S) = e^-s/s + a + e^-s/(s + a)^2