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Defining and using Heaviside’s step function in the calculator
The previous example provided some experience with the use of Dirac’s delta
function as input to a system (i.e., in the right-hand side of the ODE describing
the system). In this example, we want to use Heaviside’s step function, H(t).
In the calculator we can define this function as:
‘H(X) = IFTE(X>0, 1, 0)’ `„à
This definition will create the variable @@@H@@@ in the calculator’s soft menu key.
Example 1 -- To see a plot of H(t-2), for example, use a FUNCTION type of
plot (see Chapter 12):
• Press „ô, simultaneously in RPN mode, to access to the PLOT SETUP
window.
Change
TYPE to FUNCTION, if needed
Change EQ to ‘H(X-2)’.
Make sure that
Indep is set to ‘X’.
Press L @@@OK@@@ to return to normal calculator display.
• Press „ò, simultaneously, to access the PLOT window.
Change the H-VIEW range to 0 to 20, and the V-VIEW range to -2 to 2.
Press @ERASE @DRAW to plot the function .
Use of the function H(X) with LDEC, LAP, or ILAP, is not allowed in the
calculator. You have to use the main results provided earlier when dealing
with the Heaviside step function, i.e., L{H(t)} = 1/s, L
-1
{1/s}=H(t),
L{H(t-k)}=e
–ks
⋅L{H(t)} = e
–ks
⋅(1/s) = ⋅(1/s)⋅e
–ks
and L
-1
{e
–as
⋅F(s)}=f(t-a)⋅H(t-a).
Example 2 -- The function H(t-t
o
) when multiplied to a function f(t), i.e., H(t-t
o
)f(t),
has the effect of switching on the function f(t) at t = t
o
. For example, the
solution obtained in Example 3, above, was y(t) = y
o
cos t + y
1
sin t + sin(t-
3)⋅H(t-3). Suppose we use the initial conditions y
o
= 0.5, and y
1
= -0.25.
Let’s plot this function to see what it looks like:
• Press „ô, simultaneously if in RPN mode, to access to the PLOT
SETUP window.
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