﻿Coupled 
  Vibrations 
  : 
  Unequal 
  Masses 
  or 
  Periods. 
  63 
  

  

  Page 
  

  

  V. 
  Experimental 
  Results 
  76 
  

  

  Masses 
  20 
  : 
  1. 
  

   Logarithmic 
  Decrements. 
  

   Masses 
  5:1. 
  

   Length 
  3 
  : 
  4. 
  

   VI. 
  Sumuaby 
  78 
  

  

  I. 
  Introduction. 
  

  

  IX 
  a 
  recent 
  paper 
  * 
  two 
  types 
  of 
  coupled 
  pendulums 
  were 
  

   experimented 
  with, 
  their 
  lengths 
  and 
  the 
  masses 
  of 
  

   their 
  bobs 
  being 
  in 
  each 
  case 
  equal. 
  The 
  present 
  paper, 
  the 
  

   second 
  of 
  the 
  series, 
  deals 
  with 
  the 
  donble-cord 
  pendulum 
  

   only, 
  but 
  in 
  cases 
  where 
  either 
  the 
  masses 
  of 
  the 
  bobs 
  are 
  

   unequal 
  or 
  else 
  the 
  lengths 
  of 
  their 
  suspensions 
  are 
  unequal. 
  

  

  These 
  mechanical 
  cases 
  may 
  be 
  regarded 
  as 
  somewhat 
  

   analogous 
  to 
  the 
  electrical 
  cases 
  of 
  inductively- 
  coupled 
  circuits 
  

   with 
  unequal 
  inductances 
  or 
  unequal 
  periods 
  respectively. 
  

  

  TVith 
  unequal 
  masses 
  and 
  equal 
  lengths 
  it 
  is 
  noticeable 
  

   that 
  with 
  small 
  couplings 
  a 
  great 
  increase 
  in 
  the 
  amplitude 
  

   of 
  vibration 
  of 
  the 
  small 
  bob 
  entailed 
  very 
  little 
  loss 
  in 
  that 
  

   of 
  the 
  large 
  bob. 
  Indeed, 
  for 
  masses 
  as 
  20 
  : 
  1 
  we 
  almost 
  

   realised 
  the 
  case 
  of 
  forced 
  vibrations. 
  

  

  The 
  funnel 
  of 
  the 
  light 
  bob 
  was 
  here 
  of 
  cardboard 
  and 
  so 
  

   had 
  an 
  appreciable 
  damping. 
  This 
  rendered 
  it 
  necessary 
  to 
  

   make 
  corresponding 
  modifications 
  in 
  the 
  theory. 
  

  

  With 
  unequal 
  lengths 
  and 
  equal 
  masses 
  the 
  response 
  

   showed 
  a 
  great 
  diminution 
  for 
  small 
  couplings, 
  whereas 
  for 
  

   larger 
  couplings 
  the 
  mistuning 
  seemed 
  without 
  appreciable 
  

   effect. 
  

  

  The 
  paper 
  includes 
  twenty-seven 
  photographic 
  repro- 
  

   ductions 
  of 
  double 
  sand 
  traces 
  obtained 
  simultaneously 
  one 
  

   from 
  each 
  bob 
  of 
  the 
  coupled 
  pendulum. 
  

  

  II. 
  Theory 
  for 
  Unequal 
  Masses. 
  

   Equations 
  of 
  Motion 
  and 
  Coupling. 
  — 
  Throughout 
  the 
  work 
  

   described 
  in 
  the 
  present 
  paper 
  the 
  double-cord 
  pendulum 
  

   was 
  used. 
  This 
  was 
  shown 
  in 
  figs. 
  1, 
  2, 
  and 
  4 
  of 
  the 
  first 
  

   paper. 
  The 
  equations 
  of 
  motion 
  and 
  coupling 
  were 
  given 
  

   as 
  (27)-(29) 
  and 
  may 
  now 
  be 
  rewritten 
  here 
  as 
  follows 
  : 
  — 
  

  

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  and 
  

  

  * 
  Phil. 
  Mag. 
  (6) 
  vol. 
  xxxix. 
  no. 
  202, 
  pp. 
  246-270 
  (Oct. 
  1917). 
  

  

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