﻿G 
  = 
  tan 
  0= 
  - 
  = 
  rj. 
  

  

  (22) 
  

  

  (23) 
  

  

  Shajpness 
  of 
  Resonance 
  under 
  Sustained 
  Forcing, 
  110 
  

  

  "We 
  should 
  then 
  have 
  

  

  k 
  1 
  

  

  P 
  & 
  

  

  Reverting 
  to 
  fig. 
  1, 
  it 
  may 
  now 
  be 
  noted 
  that 
  the 
  various 
  

   curves 
  have 
  the 
  following 
  values 
  of 
  range 
  and 
  sharpness 
  : 
  — 
  

  

  G 
  = 
  0-1, 
  0-05, 
  0-03, 
  0-025, 
  0-02, 
  0*016 
  ^ 
  

   H= 
  10, 
  20, 
  30, 
  40, 
  50, 
  60 
  J 
  

  

  These, 
  it 
  will 
  be 
  seen 
  later, 
  approximate 
  to 
  some 
  of 
  the 
  

   experimental 
  examples 
  to 
  be 
  noticed. 
  In 
  the 
  diagram 
  the 
  

   values 
  of 
  H 
  are 
  inserted 
  at 
  the 
  ends 
  of 
  the 
  curves. 
  

  

  Graphs 
  for 
  Range 
  and 
  Sharpness 
  of 
  Resonance. 
  — 
  It 
  is 
  

   obvious 
  from 
  the 
  expressions 
  found 
  for 
  G 
  and 
  H 
  (see 
  

   equations 
  (21) 
  and 
  (22)), 
  that 
  when 
  h 
  is 
  constant 
  and 
  p 
  

   plotted 
  as 
  abscissa?, 
  the 
  graph 
  of 
  G 
  is 
  the 
  rectangular 
  hyper- 
  

   bola 
  xy=k 
  3 
  while 
  that 
  of 
  H 
  is 
  the 
  straight 
  line 
  y 
  = 
  x/k. 
  

  

  Fig. 
  2. 
  — 
  Graphs 
  for 
  Range 
  and 
  Sharpness 
  showing 
  their 
  Variation 
  

  

  with 
  Pitch. 
  

   SCAi.£$ 
  

  

  a 
  

  

  J? 
  

  

  1 
  

  

  ICC 
  

  

  oog 
  

  

  9Q 
  

  

  &og 
  

  

  So 
  

  

  OOJ 
  

  

  10 
  

  

  oo6 
  

  

  Go 
  

  

  o-cs 
  

  

  So 
  

  

  004 
  4-0 
  

  

  Oo3 
  So 
  

  

  OOZ 
  20 
  

  

  oot 
  Xq 
  

  

  coo 
  o 
  

  

  2» 
  =. 
  fO 
  20 
  So 
  4-o 
  So 
  6o 
  70 
  So 
  90 
  tootuiiesA 
  

  

  Ff?EC?U£/VC/£S 
  

  

  These 
  are 
  shown 
  in 
  fig. 
  2 
  over 
  about 
  the 
  same 
  ranges 
  as 
  

   in 
  fig. 
  1 
  and 
  equation 
  (23). 
  Different 
  scales 
  of 
  ordinatos 
  

  

  are 
  adopted 
  for 
  G 
  and 
  H 
  to 
  bring 
  both 
  conveniently 
  into 
  the 
  

   same 
  diagram. 
  

  

  