Lesson plan
Forcing function (differential equations)
In a system of differential equations used to describe a time-dependent process, a forcing function is a function that appears in the equations and is only a function of time, and not of any of the other variables. In effect, it is a constant for each value of t. In the more general case, any nonhomogeneous source function in any variable can be described as a forcing function, and the resulting solution can often be determined using a superposition of linear combinations of the homogeneous solutions and the forcing term. For example, f(t) is the forcing function in the nonhomogeneous, second-order, ordinary differential equation: ay + by' + cy = f(t)
Article summary
In a system of differential equations used to describe a time-dependent process, a forcing function is a function that appears in the equations and is only a function of time, and not of any of the other variables. In effect, it is a constant for each value of t. In the more general case, any nonhomogeneous source function in any variable can be described as a forcing function, and the resulting solution can often be determined using a superposition of linear combinations of the homogeneous solutions and the forcing term. For example, f(t) is the forcing function in the nonhomogeneous, second-order, ordinary differential equation: ay + by' + cy = f(t)
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Discussion questions
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