Laplace Transform Theorems - HP 50g User Manual

Example 3 – Determine the inverse Laplace transform of F(s) = sin(s). Use:
'SIN(X)' ` ILAP.
'ILAP(SIN(X))', meaning that there is no closed-form expression f(t), such that f(t)
-1
= L {sin(s)}.
Example 4 – Determine the inverse Laplace transform of F(s) = 1/s
'1/X^3' ` ILAP μ. The calculator returns the result: 'X^2/2', which is
interpreted as L
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
as follows: L {cos(a t+b)} = (s cos b – a sin b)/(s

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
for f(t), i.e., f(0) = f
Example 1 – The velocity of a moving particle v(t) is defined as v(t) = dr/dt,
where r = r(t) is the position of the particle. Let r
the transform of the velocity can be written as V(s) = L{v(t)}=L{dr/dt}= s R(s)-r
Differentiation theorem for the second derivative. Let f
= df/dt| , then L{d
t=0
The calculator takes a few seconds to return the result:
-1 3 2
{1/s } = t /2.
, then
o
L{df/dt} = s F(s) - f
2 2
f/dt } = s
2 2
+a ). The transform is interpreted
2 2
+a
.
o
= r(0), and R(s) =L{r(t)}, then,
o
2
F(s) - s f – (df/dt)
o
3
. Use:
).
be the initial condition
o
= f(0), and (df/dt)
o
.
o
.
o
o
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