Solve Laplace Transform of t sinwt w/ Theorem 1.31

JSBeckton
Messages
224
Reaction score
0

Homework Statement



Determine L{t sinwt} with the aid of therom 1.31 (its the General Differentiation method on this page: "link"[/URL]



[h2]Homework Equations[/h2]

Shown on linked page



[h2]The Attempt at a Solution[/h2]

I do not understand how to start this becasue I do not have a function to a power, I have a multiplication of 2 functions. I know there are better theorms for this porblem but he specifically said we need to use this one, can anyone help me out?

Thanks in advance.
 
Last edited by a moderator:
Physics news on Phys.org
That link is broken.
 
transform sin function then apply the corresponding laplace function of t to the transformed sin function.
 
euler_fan said:
transform sin function then apply the corresponding laplace function of t to the transformed sin function.


I don't think that is what this theorm calls for, can you verify from th link?

He said that he wants us to do it this way even though there are easier ways, go figure...
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
Back
Top