What is an 'impulsive forcing term'?

[mesa]

Google hasn't been very helpful on this one and my textbook once again assumes we are born with certain knowledge as it doesn't delve any further than, "Many practical engineering problems involve systems acted on by impulsive forcing terms" without further explanation. Isn't that nice...

So the question is; what is this? My guess is it has something to do with a force on a system for a given time (impulse) and how it is represented as some 'term' to the function itself. Is that about right?

 

[D H]

Impulsive typically means a large force that is applied over a short period of time. The quantity ∫F dt is known, but the force and the time interval over which the force is applied is not known. In the extreme, an impulsive force truly is an impulse: A Dirac delta distribution.

 

[mesa]

Impulsive typically means a large force that is applied over a short period of time. The quantity ∫F dt is known, but the force and the time interval over which the force is applied is not known. In the extreme, an impulsive force truly is an impulse: A Dirac delta distribution.

Okay so we are talking about a term in an equation that is the impulse however the Force and length of time are unknowns. Do we use the Laplace Transformations to get information on the Force and the period of time which it is applied by using the known information?

We don't get into Dirac delta functions until next week :P

 

[Chestermiller]

Think of the limit as the time interval for the application of the force shrinks to zero, while the force becomes infinite, in a way such that the integral of the force with respect to time is constant. If this takes place at time t₀, then F(t) = 0 everywhere except at t=t₀, where it's value is infinite. If I represents the impulse of the force (i.e., the integral of F(t) with respect to t from time = 0 to time = +∞, you can calculate the Laplace Transform of F(t). You can demonstrate for yourself that the Laplace Transform is equal to Ie^st₀.

 

[blue_raver22]

Yes, your understanding is correct. An impulsive forcing term refers to a sudden or short-lived force acting on a system. It is often represented as a mathematical term in equations that describe the behavior of the system. This force can come from external factors such as a sudden impact or internal factors such as a sudden change in temperature. The term "impulsive" refers to the fact that the force acts for a very short period of time compared to the overall time scale of the system. Impulsive forcing terms are important in engineering because they can cause significant changes in the behavior of a system and need to be considered in the design and analysis of systems.