forcing function

Thread Starter

PG1995

Joined Apr 15, 2011
818
Hi

I'm not proficient in calculus. I'm having problem in understanding the statement in red. I think most of the time every function reduces to a constant once you insert the value of a variable. For example, f(t) = t^2 + 2t, will reduce to a constant value once you put a certain value of "t", say t=2, in the function. Isn't it so? What am I missing here? Please let me know. Thank you

In a system of differential equations used to describe a time-dependent process, a forcing function is a function that appears in the equations and is only a function of time, not of any of the other variables. In effect, it is a constant for each value of t.
Regards
PG
 

steveb

Joined Jul 3, 2008
2,436
Hi

I'm not proficient in calculus. I'm having problem in understanding the statement in red. I think most of the time every function reduces to a constant once you insert the value of a variable. For example, f(t) = t^2 + 2t, will reduce to a constant value once you put a certain value of "t", say t=2, in the function. Isn't it so? What am I missing here? Please let me know. Thank you

Regards
PG
All they are saying is that the forcing function is only a function of time and is not a function of time and another variable or variables.

For example, you could have a function of time and space f(x,y,z,t), and if you plug in a value of t=2, the function is not a constant, but is still a function of x, y and z.
 

Thread Starter

PG1995

Joined Apr 15, 2011
818
Hi again, :)

By the way, why is this function called so? "forcing" doesn't seem to have a meaning which fits the phrase "forcing function". Could you please help? Thanks.
 

steveb

Joined Jul 3, 2008
2,436
Hi again, :)

By the way, why is this function called so? "forcing" doesn't seem to have a meaning which fits the phrase "forcing function". Could you please help? Thanks.
I think (actually I'm guessing) the terminology "forcing" comes from mechanics equations originally. In a mechanical system the input is often an actual force. By analogy, you can consider a voltage input to be like a "force" that drives the system. We even call a voltage source an electro motive force emf.

Myself, I prefer to call the forcing function an input signal because it is a more general term.
 

someonesdad

Joined Jul 7, 2009
1,583
I agree with steveb. When you take a freshman physics class, you'll be exposed to the damped harmonic oscillator with a forcing function. I've attached a photo of a page out of my Resnick & Halliday text (1966 edition) and I've underlined the forcing function. You can see that it's really a force (i.e., summed into the force terms of Newton's second law), but then things usually get written with the unknown function terms x(t) on the left and the forcing function on the right (this is a common mathematical convention). Note that the damping term \(-b \dot x\) (the overdot denotes differentiation with respect to time) depends on the velocity, so it winds up on the left side of the equation.

If you're interested, this is an equation whose behavior you could study with some free tools (python, numpy, scipy, and matplotib) -- see here if you're interested. The scipy library has routines to numerically solve the differential equations (scipy.integrate.odeint) and you could generate plots of the solutions for different values of the input parameters. This could help you develop intuition and it's an important problem, as it appears in many areas of science and technology -- for example, EEs study RCL circuits with it, mechanical engineers study bridges with it (Galloping Gertie fame), etc.

Such numerical tools allow you to experiment. For example, you might wonder how the system's behavior would change if the damping term changed its behavior on the velocity -- suppose the damping force was \(-b \dot x^{1.35}\). This turns probably the most famous elementary differential equation into one that (probably) nobody knows how to solve exactly. But you can still do a numerical integration with the numerical code -- and with a modern PC, you can have the solution virtually instantaneously.
 

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Thread Starter

PG1995

Joined Apr 15, 2011
818
Thanks a lot, Steve, someonesdad.

@someonesdad: It seems Halliday & Resnick book is quite popular the world over. My uncle has it. He also has another physics book by Young; I think it's titled University Physics. This is my uncle's opinion that Young's book is far superior than Halliday's.

Best wishes
PG
 

someonesdad

Joined Jul 7, 2009
1,583
Beauty is in the eye of the beholder... I use Resnick & Halliday because that was my freshman physics text. I paid $5 for each volume (why can I remember that?) at the bookstore, so they're paid for. In the 70's, I was working in Silicon Valley and bought Sears, Zemansky and Young's book "University Physics" at the Stanford bookstore and was quite pleased with it. It's also an excellent book (and is usually referred to as Sears and Zemansky). Both are excellent elementary texts. Saying one is better than the other is like arguing over emacs vs. vi. :)

One of the best books for a working scientist or engineer is Yavorsky and Detlaf's "Handbook of Physics", a superb little MIR book I got in the 70's for $9. But it appears to be unknown to most people. I only found out about it because a coworker had it and loaned it to me for some work problem we were discussing. After using it, I had to have a copy. At the time, the USSR was selling their books in the US at ridiculously low prices and I found this book and another superb little elementary physics book that I used a lot and would slip into a back pocket.
 

Thread Starter

PG1995

Joined Apr 15, 2011
818
Beauty is in the eye of the beholder... I use Resnick & Halliday because that was my freshman physics text. I paid $5 for each volume (why can I remember that?) at the bookstore, so they're paid for. In the 70's, I was working in Silicon Valley and bought Sears, Zemansky and Young's book "University Physics" at the Stanford bookstore and was quite pleased with it. It's also an excellent book (and is usually referred to as Sears and Zemansky). Both are excellent elementary texts. Saying one is better than the other is like arguing over emacs vs. vi. :)

One of the best books for a working scientist or engineer is Yavorsky and Detlaf's "Handbook of Physics", a superb little MIR book I got in the 70's for $9. But it appears to be unknown to most people. I only found out about it because a coworker had it and loaned it to me for some work problem we were discussing. After using it, I had to have a copy. At the time, the USSR was selling their books in the US at ridiculously low prices and I found this book and another superb little elementary physics book that I used a lot and would slip into a back pocket.
Yes, you are correct where you say beauty lies in the eyes of beholder.

By the way, what are these "emacs" and "vi". I have been to Wikipedia and it says they are text editors. I have never read about them before as far as I can remember. Text editors such as Microsoft Word you hear all the time.

Wanna share the title of that "elementary physics book"?

Thanks a lot.

Best wishes
PG
 
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