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Re: test problem

I see now that I had misread one element of Justin's problem. I
thought he had defined his origin to be at the point of release of
the mass (i.e., 25 cm below the end of the relaxed spring) rather
than at the end of the unstretched spring. As a result my earlier
remarks contain one minor (but potentialy confusing error that I
would like to correct.

I wrote:

On Tue, 4 Dec 2001, Justin Parke wrote:

...
Use conservation of energy to find the speed of the mass as it
passes through the midpoint (i.e. 12.5 cm from the origin)"

I get the same answer that you do (2.6 m/s), but I think that
the use of the word "midpoint" is highly misleading. The
midpoint of the oscillation (assuming that it somehow remains
purely vertical, which would be very unlikely) is 20 cm from
^^
(please replace with) 5

the origin--i.e., the equilibrium position. At *that* position
the speed of the mass will be 2.8 m/s. The real problem,
however, is that for the oscillation to continue, the spring
and mass will need to be constrained against "sproinging out"
as the mass continues upward and compresses the spring by 15 cm.

Because there does seem to be lingering confusion about just what
does happen. Let's summarize:

The 1.0 kg mass rests in an equilibrium position with the spring
stretched by 5.0 cm.

We find, therefore, that the spring constant is 196 N/m.

The mass is then pulled down an *additional* 20 cm and released.

As a result it oscillates with an amplitude of 20 cm around the
equilibrium position.

This requires some care to keep the spring from "sproinging"
during the upper portion of the oscillation where it will be
compressed by as much as 15 cm.

As the mass passes the position that is 12.5 cm above its release
point (7.5 cm below its equilibrium position and 12.5 cm below
the end of the unstretched spring), its speed is 2.6 m/s.

As it passes the midpoint of the oscillation (which is the same
as the equilibrium position), its speed is 2.8 m/s.

John Mallinckrodt mailto:ajm@csupomona.edu
Cal Poly Pomona http://www.csupomona.edu/~ajm