HP 48gII hp 48gII_user's manual_English_E_HDPMSG48E67_V2.pdf - Page 501

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-to) when multiplied to a function f(t), i.e., H(t-to)f(t), has the effect of switching on the function f(t) at t = to. For example, the solution obtained in Example 3, above, was y(t) = yo cos t + y1 sin t + sin(t3)⋅H(t-3). Suppose we use the initial conditions yo = 0.5, and y1 = -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. Page 16-23