Circuit analogue to Kinetic motion.

[HalfThere]

A teacher of mine assigned an extra credit problem. It involves an object falling onto some springs, and we're assigned to find highest velocity and highest acceleration. I can do that easily. However, he said that it would be double extra credit to create a circuit analogue to the problem. I'm confused. How do you create a circuit analogue to a problem based on kinetic motion?

 

[KingNothing]

It's actually quite simple and very hard to hint at, so I'll just say it.

If you have a capacitor-inductor (L-C) circuit, the overall voltage and current will oscillate according to time as the energy is transferred between the inductor's magnetic field and the capacitor's electric field.

Once you throw in a resistor, you get what is called damping. This is analogous to the friction forces acting on the mass-on-a-spring.

 

[berkeman]

Thread moved to Homework Help forums. HalfThere, please remember that homework and coursework questions need to be posted in the appropriate Homework Help forum, and should include the relevant equations, as shown in our Homework Help Template that you are provided with when you start a new thread in the Homework Help forums.

As to your question, KingNothing has given you a good start. Can you write the equation for the current and voltage in a parallel LC circuit? What can you say about the current and voltage in a parallel LC circuit as a funtion of time, assuming you start with a current I flowing through the circuit, and no voltage on the capacitor... ?

 

[cepheid]

I don't suppose the OP is familiar with second-order ordinary differential equations? Comparing the equation of motion with that governing the charge in an LRC circuit makes the analogy clear.

 

[berkeman]

I don't suppose the OP is familiar with second-order ordinary differential equations? Comparing the equation of motion with that governing the charge in an LRC circuit makes the analogy clear.

That's cool. I didn't carry the thought through to that analogy. Motion and motion!

 

[HalfThere]

I'm a bit new to the forums, so I didn't realize there was this homework board. Thanks for showing it to me.

Here's a more detailed description:

An elevator falls from a height of 15 m onto a three springs of 3 m, 2 m, and 1.5 m long respectively, and k, 2k, and 4k tension respectively, which will bring it to a stop at .5 m above the ground. I am supposed to find the maximum acceleration and velocity of the elevator in this setup. No problem.

I'm also supposed to create a circuit analogue. Unfortunately, I don't even really know where to begin. I think this was assigned to me because I happen to be in Circuit Lab in Science Olympiad (a national high-school competition, on the order of Mathletes, but for science). From that, I have learned Ohm's law, Kirchoff's Law, and resistors and capacitors, but not a word about inductors or anything else. I don't know what the purpose of a circuit analogue is, exactly, nor how it's applied nor where it is useful.

As for second-order ordinary differential equations - no clue, sorry.

 

[berkeman]

Hmmm. It gets hard to explain without differential equations and inductors. You've studied capacitors some, so you know how energy is stored in the electric field between the capacitor plates, due to the separation of charge between the plates, correct? Electrons are pumped from the positive plate to the negative plate by a battery or other voltage source, and that pumping action stores energy in the electric field between the plates. That stored energy is analogous to a spring under tension.

An inductor is a coil of wire that is wound around some magnetic metal (typically) like iron or ferrite. When a current flows through the coil of wire, a magnetic field is induced inside the metal core of the inductor. The moving current in the wire of the coil causes energy to be stored in the magnetic field in the inductor, so the movement of the electrons in the wire is analogous to the motion of an object like your elevator, and the kinetic energy of the moving object is analogous to the energy stored in the magnetic field generated by the moving electrons in the coil wire.

Make sense so far?

Now you need to think about the full analogy when the elevator hits a spring, and starts to transfer kinetic energy of motin into potential energy of the energy stored in the spring under tension. Can you make a guess as to what happens in the analogous situation when you have an inductor connected to a capacitor, and you start with zero voltage across the capacitor, and some current I flowing in the inductor?