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The result is:
‘SIN(X-3)*Heaviside(X-3) + cC1*SIN(X) + cC0*COS(X)’.
Please notice that the variable X in this expression actually represents the
variable t in the original ODE. Thus, the translation of the solution in paper may
be written as:
When comparing this result with the previous result for y(t), we conclude that
cC
o
= y
o
, cC
1
= y
1
.
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.
Θ 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 .
)3()3sin(sincos)(
1
−⋅−+⋅+⋅= tHttCtCoty