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A function is one of the most fundamental ideas in mathematics. At its core, a function describes a rule that takes an input and assigns it exactly one output. You can think of it as a machine: you put a value in, the function processes it according to a fixed rule, and a result comes out. This idea allows mathematicians to describe relationships between quantities, such as how distance depends on time or how the area of a shape depends on its dimensions. Functions help turn real-world situation
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Let’s find the transfer function for this translational mechanical system. Here, we have a mass-spring-damper system. It is clear that the input is the force 𝑓(𝑡) and the output is the displacement 𝑥(𝑡). The restoring force of the Hookean spring, along with the viscous damping force, impede the motion brought about by the forcing function 𝑓(𝑡). By drawing a free-body force diagram, we can use Newton’s Second Law to set up a second-order differential equation which formulates a dynamic mode
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