Inverse laplace transform without partial fractions

Click For Summary
The discussion centers on finding the inverse Laplace transform of the function 6/[s^4(s-2)^2]. One participant suggests using partial fractions but questions whether the expression can be manipulated for use with the Laplace table. Another participant proposes rewriting the function as 6/s^4 multiplied by 1/(s-2)^2, allowing for the use of table methods and convolution to obtain the inverse transform. The overall consensus is that while partial fractions are a common approach, alternative methods like the Bromwich integral or convolution may also be viable. The discussion highlights the flexibility in methods for solving inverse Laplace transforms.
shreddinglicks
Messages
225
Reaction score
7

Homework Statement


take inverse laplace of:

6/[s^4(s-2)^2]

Homework Equations


6/[s^4(s-2)^2]

The Attempt at a Solution


I used partial fractions. I was wondering if It could be manipulated to where I could use the laplace table?
 
Physics news on Phys.org
If you don't want to use partial fractions, you could evaluate the Bromwich integral:
$$\frac{1}{2\pi i}\int_{\sigma-i\infty}^{\sigma+i\infty} \frac {6 e^{st}}{s^4(s-2)^2}\,ds$$
 
shreddinglicks said:

Homework Statement


take inverse laplace of:

6/[s^4(s-2)^2]

Homework Equations


6/[s^4(s-2)^2]

The Attempt at a Solution


I used partial fractions. I was wondering if It could be manipulated to where I could use the laplace table?
You could write it as$$
\frac 6 {s^4}\cdot \frac 1 {(s-2)^2}$$inverse both factors using table methods, and take the convolution for your answer. Not sure it would be any easier though.
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

Similar threads

  • · Replies 10 ·
Replies
10
Views
2K
  • · Replies 1 ·
Replies
1
Views
1K
Replies
9
Views
2K
  • · Replies 6 ·
Replies
6
Views
1K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 4 ·
Replies
4
Views
3K
Replies
2
Views
2K
  • · Replies 1 ·
Replies
1
Views
1K
Replies
5
Views
2K