What is the most impactful way of introducing Laplace transforms?

[matqkks]

I am trying to find a motivating way to introduce Laplace transforms to engineering students. Looking for concrete examples where they might need Laplace transforms.

 

[DaveE]

It is THE main tool for linear systems analysis (often non-linear systems too). Analog circuit design, filter design, control systems, state space analysis, etc. We do nearly everything in the s domain. Also nearly the only good way to do transient analysis in linear systems. It's all about the poles and zeros in the Laplace transfer function.

In my world the impedance of an inductor isn't L, it's sL. Linear circuit analysis starts and often ends in the s domain, you transform back to time only when you have to.

 

[Mark44]

Laplace transforms are also useful in solving nonhomogeneous ODES such as those that describe LRC electrical circuits with an AC driving voltage. These transforms are also useful in solving ODEs that describe mechanical systems that involve a spring, mass, and damping device, and that have a driving force acting on them.

 

[DaveE]

I might also mention, but not teach, the z-transform. It's essentially the Laplace equivalent for discrete time systems; digital controls and such. Just to show that it's not a one-off tool, it's a fundamental way of thinking about analysis.

 

[berkeman]

motivating way to introduce Laplace transforms to engineering students.

What kind of Engineering students? Are they EEs? If so, as @DaveE says Laplace Transforms are used in most of circuit analysis. If they are mostly MEs or some other type of engineering, we probably need to think more about good applications that are used in their specialty.

 

[wrobel]

I am trying to find a motivating way to introduce Laplace transforms to engineering students. Looking for concrete examples where they might need Laplace transforms.

linear ode with delay for example

 

[FactChecker]

Aero engineers in flight control design or stability and control use it heavily.