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Re: [Phys-l] Mass and SHO amplitude Was: Re: Student Misconceptions



On 10/08/2011 09:29 AM, Bernard Cleyet wrote:
I'm not going to bother checking if I was explicit that this was an
ideal (simple) pendulum wherein it is a linearized one. One
respondent did mention the small angle approximation. So the
equations are then the same.

That's not the point.

The point is that changing the mass of a pendulum
necessarily changes the restoring force in equal
measure ... leaving the period unchanged, provided
the mass was added in such a way as to leave the length
unchanged ... and indeed it would be equally easy to
add mass to the bottom (increasing the length) as to
add it to the top (decreasing the length).

This stands in stark contrast to the mass on a
spring, where adding mass leaves the spring unchanged,
and always lowers the frequency in proportion to the
square root of the mass.

the equations are then the same.

The equations are not the same. With or without the
small-angle approximation, the physics is not the
same. The equivalence of gravitational mass and
inertial mass is a deep principle of physics. It
applies to pendulums and not to springs.

Intuitively if added on the "down swing" the amplitude will be
increased and visa versa.

That's not what my intuition says. Basically it's
just a mess, because if the added mass carries
momentum it disturbs the system, and if it doesn't
carry momentum it disturbs the system.

I spent several days in an attempt to drop a hanging mass from a
bob. My app. consisted of an EM powered by a solar cell. when I
shut off the lamp the weight dropped. It was, of course
unsuccessful, because of the retentivity of the EM's core.

So get a more suitable core. Ferrite cores work just fine up
to megahertz frequencies, which really ought to be fast enough.
And/or invert the mechanism so that turning the magnet *on*
pulls a pin, thereby releasing the load. Electric latches
(including door latches) and electric bomb shackles have been
around for a long time. Back in the 1960s PSSC did a lot by
holding stuff together with a thread, and then burning the
thread. Bottom line: This part of the problem shouldn't be
a stumbling block.