Laplace Transform 4

Part 2 of getting the Laplace transform of sin(at)

Category:

Education

Tags:

• Laplace
• Transform

[Frahm12]

shouldnt it be plus after he factored out - e^(-st )

[a13x4]

Around the line when you substitute in for y,

you've made a mistake when you rewrite it as

y+a^2/s^2 y = -e^(-st)(sinat/s - 1/s^(2) (cos(at))

As you've missed out the fact that in the line before you have a/s^2 * e^-st (cosat)

So shouldn't it be y+a^2/s^2 y = -e^(-st)(sinat/s - a/s^(2) (cos(at))

[longname3141]

This is an Ahhhhhhhhhhhhhhhhhh

[HolySsshaco]

Oops added another squiggle, well that was unnecessary! Really easy to follow!

[sagatyba]

o no

[shastanguyen1]

Ahhhhhh I love the Kahn academy! -3

[kevinbs05]

So, this is diff eq, so why not use complex numbers to integrate. Substitute sin(at) for (1/(2i)* (e^(iat) - e^(-iat)); then you still get -e^(-st)/(a^2 + s^2) * ( a*cos(at) + s*sin(at)).

[MrCouscousable]

@a13x4 No, it would be y+a^2/s^2 y = -e^(-st)(sinat/s + a/s^(2) (cos(at)), which he corrected towards the end of the video.

[ahmoodloova]

simple method=

we all know--> cos t=1/2[e^jt+e^-jt] ,we can use that to solve

so it will be F(s)= (integration of cos t .e^-st)=

integration of (1/2[e^jt+e^-jt].e^-st)=

i/2[(1/s-j)+(1/s+j)]...=s/s^2+­1^2

its much easier than all of that ^_^

[omgthatscrazyx]

The Great Khan

[TaaSv3n]

Damn Vaninsky! ima kill u!.. u make Laplace look soo hard!! this $#!t is Easy! Thanks Mr. Khan... Really helpful... and Clear!

[TaaSv3n]

Damn Vaninsky! ima kill u!.. u make Laplace look soo hard!! this $#!t is Easy!