lab7B - Lab 7B: Laplace Transforms in Matlab Recall the...

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Page 1 - 7 Be sure to declare all the symbolic variables using syms . Lab 7B: Laplace Transforms in Matlab Recall the Laplace transform of the function f ( t ) is: F ( s ) = f ( t ) e 0 " # $ st dt Many transforms can be evaluated using Matlab's laplace command. The only tricky part is to be sure to declare all the required symbolic variables. Syntax: > laplace(f) Open a new session in Matlab. Exercise 1. You can easily find Laplace transforms using the command laplace from Matlab's symbolic toolbox. Be sure to remember to declare the variables as symbolic quantities. As an example, find the laplace transform of the linear term f ( t ) = t . Note this is the same as the ramp function r ( t ) since the Laplace transform is one-sided. a. In Matlab enter the following commands. > syms f t > f = t > F = laplace(f) which yields F = 1/s^2 Using this same method, find the laplace transform for each of the following monomial functions. Record your answers for credit. i. f 1 ( t ) = t 2 ii. f 2 ( t ) = t 3 iii. f 3 ( t ) = t 4 i. F1 = …. ii. F2 = …. iii. F3 = …. Based on your results make a guess for the laplace transform of f ( t ) = t n , for t > 0. b. Matlab can also find laplace transforms for functions with symbolic variables as illustrated in this example. Find the laplace transform of f ( t ) = e " at . > syms a t f > f = exp(-a*t) > F = laplace(f) which yields F = 1/(s+a)
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Page 2 - 7 Using this same method, find the laplace transform for each of the following functions which have symbolic variables in their expressions. Record your answers for credit. i. f 1 ( t ) = t e " at ii. f 2 ( t ) = b + t ( ) e " at iii. f 3 ( t ) = sinh( a t ) i. F1 = …. ii. F2 = …. iii. F3 = …. Answers are shown below, but are not in order. a/(s^2-a^2) 1/(s+a)^2 b/(s+a)+1/(s+a)^2 Exercise 2. The inverse transform is found using Matlab's ilaplace command. Compute the inverse Laplace transform of:
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lab7B - Lab 7B: Laplace Transforms in Matlab Recall the...

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