PASCO ME-6828 Dynamics Cart Magnetic Damping User Manual

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E x p e r i m e n t 2 : C r i t i c a l D a m p i n g

Data Collection

Pull the cart up the track exactly to the mark.

Release the cart and start data recording at the same time.

Wait until the cart stops.

Stop data recording.

Move the magnets up by about 1 mm to make the system under-damped.

Repeat steps 1 through 4.

Move the magnets down as close to the track as you can get them (without touch-
ing) to make the system over-damped.

Repeat steps 1 through 4.

Question

What type of damping (under, over, or critical) makes the cart stop in the shortest
time?

Further Study: What factors affect critical damping?

You have already discovered that reducing the height of the magnets can change the
system from under-damped to critically damped to over-damped. What other factors
can you adjust to change the system’s damping behavior?

Starting with a critically damped system each time, make the following changes to the
system and observe the result.

•

Release the cart from a different position on the track.

•

Add about 20 g of mass to the cart.

•

Change the angle of the track.

•

Change the spring constant (replace or remove one of the springs).

Further Study: Theoretical model

For the theoretical model of the cart’s position as a function of time, we will assume
that the spring is massless and obeys Hooke’s law; that the damping force is propor-
tional to velocity; and that there are no forces acting on the cart other than the spring
force, the damping force, the force of gravity, and the normal force of the track. We
will also set the condition that the initial velocity

at time

. The

motion of the cart is determined with the following quantities:

x, the position of the cart with

at the equilibrium position

, the initial position at time

m, the mass of the cart

k, the spring constant (

)

v 0

( )

spring

–