HP 48gII hp 48gII_user's manual_English_E_HDPMSG48E67_V2.pdf - Page 520

Fourier series applications in differential equations Suppose we want to use the periodic square wave defined in the previous example as the excitation of an undamped spring-mass system whose homogeneous equation is: d2y/dX2 + 0.25y = 0. We can generate the excitation force by obtaining an approximation with k =10 out of the Fourier series by using SW(X) = F(X,10,0.5): We can use this result as the first input to the function LDEC when used to obtain a solution to the system d2y/dX2 + 0.25y = SW(X), where SW(X) stands for Square Wave function of X. The second input item will be the characteristic equation corresponding to the homogeneous ODE shown above, i.e., 'X^2+0.25' . With these two inputs, function LDEC produces the following result (decimal format changed to Fix with 3 decimals). Pressing ˜ allows you to see the entire expression in the Equation writer. Exploring the equation in the Equation Writer reveals the existence of two constants of integration, cC0 and cC1. These values would be calculated using initial conditions. Suppose that we use the values cC0 = 0.5 and cC1 = -0.5, we can replace those values in the solution above by using function SUBST (see Chapter 5). For this case, use SUBST(ANS(1),cC0=0.5) `, followed by SUBST(ANS(1),cC1=-0.5) `. Back into normal calculator display we can use: Page 16-42