Laplace transform of phase-shifted sinusoid

  • #1
869
4

Homework Statement


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

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:

Answers and Replies

  • #2
193
2
Use trig summation identity to simplify:

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

Can you finish from here?
 
  • #3
275
0
When your step function starts, at t=0 ?
 

Related Threads on Laplace transform of phase-shifted sinusoid

  • Last Post
Replies
1
Views
5K
  • Last Post
Replies
5
Views
962
  • Last Post
Replies
3
Views
678
  • Last Post
Replies
4
Views
895
  • Last Post
Replies
6
Views
1K
  • Last Post
Replies
7
Views
1K
  • Last Post
Replies
11
Views
956
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
2
Views
476
Top