laplace transforms

Use the unit step function to express the function http://webwork.math.ttu.edu/webwork2...18af0996c1.png and then find the Laplace Transform http://webwork.math.ttu.edu/webwork2...7ebbecd6c1.png

http://webwork.math.ttu.edu/webwork2...e50a7a1d91.png

Find the Laplace transform http://webwork.math.ttu.edu/webwork2...7ebbecd6c1.png of http://webwork.math.ttu.edu/webwork2...18af0996c1.png

http://webwork.math.ttu.edu/webwork2...04fcb1edd1.png


http://webwork.math.ttu.edu/webwork2...518da98141.png

Quote:

---

Originally Posted by dbhakta

Use the unit step function to express the function http://webwork.math.ttu.edu/webwork2...18af0996c1.png and then find the Laplace Transform http://webwork.math.ttu.edu/webwork2...7ebbecd6c1.png

http://webwork.math.ttu.edu/webwork2...e50a7a1d91.png

Find the Laplace transform http://webwork.math.ttu.edu/webwork2...7ebbecd6c1.png of http://webwork.math.ttu.edu/webwork2...18af0996c1.png

http://webwork.math.ttu.edu/webwork2...04fcb1edd1.png

http://webwork.math.ttu.edu/webwork2...518da98141.png

---

just use the definition of th laplace transform(or you could memorize a theorem)

for the first one







do the same thing for the 2nd one. Good luck.

First you need to convert the information given in the form of range to heaviside:

f(t) = 0, 0 < t < 2;
→ 0.[H(t-0) - H(t-2)]
= 0

f(t) = (t+1), t > 2;
→ (t+1). H(t+2)
[(t-2)+3].H(t-2)
(t-2)H(t-2) + 3H(t-2)

then you apply laplace transform to each of the terms above:

for the first term you will get: 0
for the second term you will get(using table):
exp(-2s)/(s^2) +3 exp(-2s)/s


for the second part just change (t+1) to 1 and repeat the steps again.
and yeah you can always use the general method posted by TheEmptySet.