## PSN-L Email List Message

Subject: RE: Lengthening a vertical period with pulley
From: "John D Nelson" jnelson@.................
Date: Fri, 2 May 2003 07:48:03 -0500

```You nailed the flaw in my logic right away.  I wasn't thinking about the
fact that weight would be reduced by the factor of the mechanical
advantage.  My thinking was using the same weight which wouldn't work.
Thanks for kick in the head.

=20

John Nelson

=20

-----Original Message-----
From: ChrisAtUpw@....... [mailto:ChrisAtUpw@...........
Sent: Thursday, May 01, 2003 7:16 PM
To: psn-l@..............
Subject: Re: Lengthening a vertical period with pulley

=20

In a message dated 01/05/03, jnelson@................. writes:=20

Has anybody ever thought of lengthening the period of a vertical with a
pulley arrangement like a compound bow. =20

Hello John,=20

You could use a mass hung from an eccentric pulley which is
suspended on a horizontal torsion rod, to give an extended period.
Essentially you are balancing the rate of change in rotational torque
from the rod with a variable mechanical advantage to obtain a small
angle over which the resultant rotational restoring force is nearly
constant. This 'bow type' application has been done successfully.=20

Seems to me that If you took the basic LaCoste arrangement and fixed the
spring=20

where the weight would ordinarily be, placed a multiple pulley from the
spring to the top point and then hung the weight on the cable to the
pulley, the period would lengthen times the amount of the mechanical
advantage.  Ideally the best medium instead of rope would be flat metal
tape.  The only problem I see is friction in the bearings of the pulleys
lowering the sensitivity of the instrument.  Has this ever been done?

Can you explain a bit more clearly why you think your proposal
should extend the period, please? If you have a constant spring force
and use a mechanical advantage of n, you will need 1/n of the original
mass to balance the system. Do you have a pictorial reference for the
type of bow you are considering, please? There are some very complicated

The LaCoste compensation system depends on the spring having a
zero length when it is unloaded. Practical springs are tightly coiled
and you have to put an appreciable force on them before they extend at
all. It is possible to use a strongly bent leaf spring which has the
same extension / force rate on the underside of the LaCoste beam. See
Sean Morrissey's STM-8 vertical seismometer.=20

Regards,=20

Chris Chapman

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You nailed the flaw in my logic =
right
away.  I wasn’t thinking about the fact that weight would be =
reduced
by the factor of the mechanical advantage.  My thinking was using =
the same
weight which wouldn’t work.  Thanks for kick in the =

John Nelson

-----Original =
Message-----
From: ChrisAtUpw@.......
[mailto:ChrisAtUpw@........
Sent: Thursday, May 01, =
2003 7:16
PM
To: =
psn-l@..............
Subject: Re: Lengthening =
a
vertical period with pulley

In a message dated =
01/05/03,
jnelson@................. writes:

Has anybody ever thought of
lengthening the period of a vertical with a pulley arrangement like a =
compound
bow.

Hello John, =

You could use a mass hung from an =
eccentric
pulley which is suspended on a horizontal torsion rod, to give an =
extended
period. Essentially you are balancing the rate of change in rotational =
torque
from the rod with a variable mechanical advantage to obtain a small =
angle over
which the resultant rotational restoring force is nearly constant. This =
'bow
type' application has been done successfully.

Seems to me that If you took the basic LaCoste arrangement and fixed the =
spring

where
the weight would ordinarily be, placed a multiple pulley from the spring =
to the
top point and then hung the weight on the cable to the pulley, the =
period would
lengthen times the amount of the mechanical advantage.  Ideally the =
best
medium instead of rope would be flat metal tape.  The only problem =
I see
is friction in the bearings of the pulleys lowering the sensitivity of =
the
instrument.  Has this ever been done?

Can you explain a bit more clearly =
why you
think your proposal should extend the period, please? If you have a =
constant
spring force and use a mechanical advantage of n, you will need 1/n of =
the
original mass to balance the system. Do you have a pictorial reference =
for the
type of bow you are considering, please? There are some very complicated

The LaCoste compensation system =
depends on
the spring having a zero length when it is unloaded. Practical springs =
are
tightly coiled and you have to put an appreciable force on them before =
they
extend at all. It is possible to use a strongly bent leaf spring which =
has the
same extension / force rate on the underside of the LaCoste beam. See =
Sean
Morrissey's STM-8 vertical seismometer.

Regards,

Chris Chapman

```