Posted by Mike on Sunday, May 3, 2009 at 5:05pm.
What is the laplace transform of (t^2)sin(t)?
- Math - Count Iblis, Sunday, May 3, 2009 at 5:31pm
f(s) = integral from t = 0 to infinity of t^2 sin(t) exp(-s t) dt
To compute this integral consider first the Laplace transform of exp(i t). Using the fact that the integral from zeo to infinity of exp(-alpha t) is 1/alpha, you find that this is:
1/(s - i)
The Laplace transform of sin(t) then follows by taking the imaginary part of this:
Im[1/s-i] =Im[(s+i)/(s^2+1)] = 1/(s^2+1)
If you differentiate this twice w.r.t. s, you bring down a factor of t^2 in the integrand of the Laplace integral. So, the Laplace thransform is given by:
8 s^2/(s^2+1)^3 - 2/(s^2+1)
- Math - Count Iblis, Sunday, May 3, 2009 at 6:19pm
Typo in last formula: The Laplace transform is:
8 s^2/(s^2+1)^3 - 2/(s^2+1)^2
Answer this Question
More Related Questions
- calc 2 - (last one) ... Let f(t) be a function defined for all values of t. The...
- Calc2 - Let f(t) be a function defined for all values of t. The Laplace ...
- math - solve y"+4y-4z'=3x z"+z-y'=1-x where y(0)=z(0)=1 and y'(0)=z'(0)=0 by ...
- advanced math - what is the Laplace transform of e^4t(cos 2t) ?
- college math - the Laplace transform of e^4t(cos 2t)?? please i need help. ...
- ODE - what is the laplace transform of 5/2.e^t-3/2.e^-t
- Calc 3 - What is the laplace transform of: f(t) = 0, 0<t<2 t, 2<t ...
- Math - Using the table Laplace transform, determine the function f (t) of the ...
- Calculus - Find the Laplace transform of: f(t)=t-2e^(3t)
- Calculus - Find the inverse Laplace transform of: F(s)=3/(s-4)