Differential equation to transfer function

1. How do you convert differential equations to transfer functions?
2. What is transfer function equation?
3. How are transfer functions derived?

How do you convert differential equations to transfer functions?

Transfer Function to Single Differential Equation

To find the transfer function, first write an equation for X(s) and Y(s), and then take the inverse Laplace Transform. Recall that multiplication by "s" in the Laplace domain is equivalent to differentiation in the time domain.

What is transfer function equation?

The transfer function of a system is defined as the ratio of Laplace transform of output to the Laplace transform of input where all the initial conditions are zero. Where, T(S) = Transfer function of the system. C(S) = output.

How are transfer functions derived?

It is obtained by applying a Laplace transform to the differential equations describing system dynamics, assuming zero initial conditions. In the absence of these equations, a transfer function can also be estimated from measured input-output data.