Menu Close

calculate-L-e-2x-sin-x-real-and-L-laplace-transform-

Tinku Tara 0 Comments
Pin




Question Number 60681 by maxmathsup by imad last updated on 24/May/19
calculate L(e^(−2x) sin(αx)) α real and L laplace transform
calculateL(e−2xsin(αx))αrealandLlaplacetransform
Commented by maxmathsup by imad last updated on 26/May/19
L(e^(−2x) sin(αx)) =∫_0 ^∞ f(t)e^(−xt) dt =∫_0 ^∞ e^(−2t) sin(αt) e^(−xt) dt =∫_0 ^∞ e^(−(x+2)t) sin(αt)dt =Im(∫_0 ^∞ e^(−(x+2)t) e^(iαt) dt) ∫_0 ^∞ e^(−(x+2)t) e^(iαt) dt =∫_0 ^∞ e^((−(x+2) +iα)t) dt =[(1/(−(x+2) +iα)) e^(−{(x+2)+iα}) ]_0 ^∞ =(1/(x+2−iα)) =((x+2 +iα)/((x+2)^2 +α^2 )) ⇒ L (e^(−2x) sin(αx)) = (α/((x+2)^2 +α^2 )) .
L(e−2xsin(αx))=∫0∞f(t)e−xtdt=∫0∞e−2tsin(αt)e−xtdt=∫0∞e−(x+2)tsin(αt)dt=Im(∫0∞e−(x+2)teiαtdt)∫0∞e−(x+2)teiαtdt=∫0∞e(−(x+2)+iα)tdt=[1−(x+2)+iαe−{(x+2)+iα}]0∞=1x+2−iα=x+2+iα(x+2)2+α2⇒L(e−2xsin(αx))=α(x+2)2+α2.

Pin

Leave a Reply

Your email address will not be published. Required fields are marked *