HP 48gII - Manual (Page 490)

Page 16-12
function LAP you get back a function of X, which is the Laplace transform of
f(X).
Example 2 – Determine the Laplace transform of f(t) = e
2t ⋅sin(t). Use:
‘EXP(2*X)*SIN(X)’ ` LAP The calculator returns the result: 1/(SQ(X-2)+1).
Press µ to obtain, 1/(X 2 -4X+5).
When you translate this result in paper you would write
5 4
1
} sin { ) (
2
2
+ ⋅ −
= ⋅ =
s s
t e s F t L
Example 3 – Determine the inverse Laplace transform of F(s) = sin(s). Use:
‘SIN(X)’
` ILAP. The calculator takes a few seconds to return the result:
‘ILAP(SIN(X))’, meaning that there is no closed-form expression f(t), such that f(t)
= L
-1 {sin(s)}.
Example 4 – Determine the inverse Laplace transform of F(s) = 1/s
3 . Use:
‘1/X^3’ ` ILAP µ. The calculator returns the result: ‘X^2/2’, which is
interpreted as L -1 {1/s 3 } = t 2 /2.
Example 5 – Determine the Laplace transform of the function f(t) = cos (a
⋅t+b).
Use: ‘COS(a*X+b)’ ` LAP . The calculator returns the result:
Press µ to obtain –(a sin(b) – X cos(b))/(X 2 +a 2 ). The transform is
interpreted as follows: L {cos(a ⋅t+b)} = (s⋅cos b – a⋅sin b)/(s 2 +a 2 ).
Laplace transform theorems
To help you determine the Laplace transform of functions you can use a
number of theorems, some of which are listed below. A few examples of the
theorem applications are also included.
• Differentiation theorem for the first derivative. Let f
o
be the initial condition
for f(t), i.e., f(0) = f
o
, then