1. The Laplace Transform

2. The Laplace Transform table

3. Transfer Function

4. Transfer function Transfer function
The transfer function of a linear, time-invariant , differential equation system is defined as the ratio of the Laplace transform of the output (response function) to the Laplace transform of the input (driving function) under the assumption that all initial conditions are zero.
Consider the linear time-invariant system defined by the following differential equation:
Transfer function=

5. To find the transfer function
To derive the transfer function, we proceed according to the following steps.
Write the differential equation for the system.
Take the Laplace transform of the differential equation, assuming all initial conditions are zero.
Take the ratio of the output to the input. This ratio is the transfer function.
Now consider some simple cases of finding transfer function

6. Differential Equation of Physical Systems
Electrical Inductance
Describing Equation
Energy or Power
Translational Spring
Rotational Spring
Fluid Inertia

7. Differential Equation of Physical Systems
Electrical Capacitance
Translational Mass
Rotational Mass
Fluid Capacitance
Thermal Capacitance

8. Differential Equation of Physical Systems

9. Differential Equation of Physical Systems

10. Block Diagram
Block Diagrams. A block diagram of a system is a pictorial representation of the functions performed by each component and of the flow of signals.
The functional block or simply block is a symbol for the mathematical operation on the input signal to the block that produces the output. The transfer functions of the components are usually entered in the corresponding blocks.