## PSN-L Email List Message

Subject: Re: Lengthening a vertical period with pulley
From: ChrisAtUpw@.......
Date: Thu, 1 May 2003 20:15:56 EDT

```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

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
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 compo=
und bow.

Hello John,

You could use a mass hung from an e=
ccentric pulley which is suspended on a horizontal torsion rod, to give an e=
xtended period. Essentially you are balancing the rate of change in rotation=
al torque from the rod with a variable mechanical advantage to obtain a smal=
l angle over which the resultant rotational restoring force is nearly consta=
nt. 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 weigh=
t would ordinarily be, placed a multiple pulley from the spring to the top p=
oint and then hung the weight on the cable to the pulley, the period would l=
engthen times the amount of the mechanical advantage.  Ideally the best=
medium instead of rope would be flat metal tape.  The only problem I s=
ee is friction in the bearings of the pulleys lowering the sensitivity of th=
e instrument.  Has this ever been done?

Can you explain a bit more clearly=20=
why you think your proposal should extend the period, please? If you have a=20=
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 referen=
ce for the type of bow you are considering, please? There are some very comp=

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

Regards,

Chris Chapman
```