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
Printable View
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
just use the definition of th laplace transform(or you could memorize a theorem)Quote:
Originally Posted by dbhakta
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.
