LAPLA CE TRANS TRANSFORM FORM BY DI RECT RECT I NTEGRATI NTEGRATI ON: Problem 01
Find the Laplace transform of
when
.
Solution 01
Thus, answer Thus,
Problem 03
Find the Laplace transform of answer Solution 03 Problem 02
Find the Laplace transform of Solution 02
.
.
For
Using integration by parts:
. Let
Thus,
Using integration by parts again. Let
Therefore, answer
LI NEARI TY PROPERTY | LA PLACE TRANSFORM: Problem 04
Find the Laplace transform of
.
Solution 04
answer Problem 05
By using the linearity property, show that
Solution 05
okay FI RST SHIF TING PROPERTY OF LA PLACE TRANSFORM: Problem 06
Find the Laplace transform of
.
But Solution 06
Thus,
Thus, From the table of Laplace transform, and Hence,
answer Problem 07
Find the Laplace transform of Solution 07
.
Thus,
Thus, answer Problem 08
Find the Laplace transform of
.
Solution 08
answer SECOND SHI FTI NG PROPERTY OF LA PLACE TRANSFORM : Problem 10
Find the Laplace transform of Solution 10
Thus,
and
Thus,
answer Problem 09
Find the Laplace transform of Solution 09
. answer
Problem 11
Find the Laplace transform of Solution 11
and answer Problem 13
Find the Laplace transform of
.
Solution 13
Thus,
answer MUL TIPLI CATION BY PO WER OF ‘t’ : Problem 12
Find the Laplace transform of
.
Solution 12
answer Problem 14
Find the Laplace transform of
Solution 14
answer DIVISION BY ‘t’ |
LAPLA CE TRANSFORM:
Problem 15
Find the Laplace transform of Solution 15
Let
Hence,
.
Solution 16
Since Thus,
and
Then,
answer Problem 16
Find the Laplace transform of
.
Since and
Then,
answer Problem 17
Find the Laplace transform of Solution 17
.
Then,
answer Problem 18
Find the Laplace transform of Solution 18
Since
.
Solution 20
..........
answer LAPLA CE TRANSFORM OF DERI VATI VES: Problem 19
Find the Laplace transform of derivatives.
using the transform of
Solution 19
..........
..........
answer
..........
Problem 21
Find the Laplace transform of derivatives. Solution 21
..........
answer Problem 20
Find the Laplace transform of derivatives.
using the transform of
using the transform of
Problem 22
Problem 23
Find the Laplace transform of derivatives.
using the transform of
Solution 22
Find the Laplace transform of
if
.
Solution 23 ..........
.......... Since,
Then,
answer Problem 24
Find the Laplace transform of Solution 24
answer LAPLA CE TRANSFORM OF I NTEGRALS:
Hence,
.
answer Problem 25
Find the Laplace transform of Solution 25
answer EVALUA TION OF I NTEGRALS: Problem 26
Evaluate Solution 26
Since and From division by t:
Then,
Therefore, answer Problem 28
Find the value of Solution 28
Therefore, answer
By "first shifting property" of Laplace transformation:
Problem 27
Find the value of
.
Solution 27
Therefore,
From "multiplication by power of t":
Therefore, answer I NVERSE L APLACE TRANSFORM: Problem 30
Find the inverse transform of
.
Solution 30
answer Problem 29
Evaluate
.
Solution 29
By first shifting property:
answer Problem 31
Thus,
Find the inverse transform of Solution 31
.
For
set set answer
Thus,
Problem 32
Find the inverse transform of
.
Solution 32
answer Problem 34
Find the inverse transform of Solution 34
Factor the denominator by factor theorem answer
is a factor
→
Problem 33
Perform the indicated operation: Solution 33
→
→
is a factor is a factor
Thus,
For
Set
Set
Set
Therefore,
answer
