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__Walk-Through__

As a warm up, we look at damped motion *without* a spring.

Set *k*_{1} = *k*_{2} = 0,
*m*_{1} = *m*_{2} = 2,
*v*_{1} = 1.2, *v*_{2} = 0.6, *b* = 5.

The masses come to rest. Approximately how long did that take? How much further did the faster one get?

How do you predict this will change if we halve the damping? Check it out!

Can you guess what the formula looks like for distance traveled? Apart from a constant, the formula can be found just using dimensions. Try it. What about a characteristic time?

Now bring in the spring.

Leave *k*_{1} = 0, but put *k*_{2} = 0.3,
*v*_{1} = *v*_{2} = 1.2.
Everything else the same. First predict how this will affect the terms, then press play. Describe the difference the spring makes. This brings in another time constant: time of decay. Find how long it takes to drop to half its maximum displacement. Find how this changes on varying the mass, the spring constant, and the damping.

Here's the relevant lecture.

*Program by: Carter Hedinger*