Laplace transform of phase-shifted sinusoid

KingNothing
Messages
880
Reaction score
4

Homework Statement


Find the laplace transform of f(t)=sin(4t+\frac{\pi}{3})u(t).
http://img822.imageshack.us/img822/6996/codecogseqna.gif

Uploaded with ImageShack.us


Homework Equations


Definition of laplace transform, and properties: http://en.wikipedia.org/wiki/Laplace_transform#Properties_and_theorems"


The Attempt at a Solution


I have a feeling that I need to use the time-shift property of the transform, but I need just a bit more direction on the strategy.
 
Last edited by a moderator:
Physics news on Phys.org
Use trig summation identity to simplify:

f(t) = \left[ sin(4t)cos(\frac{\pi}{3}) + cos(4t)sin(\frac{\pi}{3}) \right] u(t).

Can you finish from here?
 
When your step function starts, at t=0 ?
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

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...
View full post »

Similar threads

A tricky inverse Laplace transform
Replies
8
Views
2K
Inverse Laplace Transformation
Replies
1
Views
1K
Solving ODE with Laplace transform
Replies
7
Views
2K
Laplace transform of Heaviside function
Replies
3
Views
3K
Laplace tranform of unitstep (heaviside) function
Replies
1
Views
1K
ODE: Solving using Laplace Transform
Replies
3
Views
1K
Laplace Transform: Find $$z(t)$$
Replies
3
Views
1K
Keep getting the wrong answer in this lengthy Laplace problem
Replies
8
Views
2K
Heaviside and Laplace Transforms
Replies
13
Views
3K
So the inverse transform of \frac{3s+ 5}{s^2+ 9} is 3cos(3x)+ (5/3)sin(3x).
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top