Lab:  Simple  Pendulums    A  simple  pendulum  is  a  point  mass  hanging  from  a  very  light  string  or  wire  from  a  fixed  point,  swinging  back  and  forth  about  that  point  due  to  gravity.    The  period  of  a  pendulum  is  the  time  it  takes  the  pendulum  to  undergo  one  oscillation  –  that  is  the  time  it  takes  to  swing  from  one  side  to  the  other  side  and  back.    Your  goal  in  this  experiment  is  to  determine  what  determines  the  period  of  simple  pendulum  and  how.    The  first  day  of  the  lab  you  will  divide  into  groups  of  approximately  four  to  brainstorm.  Consider  the  factors  of  the  pendulum.    Determine  what  factors  you  think  may  control  the  period.  Examine  the  available  equipment.    Devise  a  method  to  manipulate  one  of  those  factors  while  keeping  the  remaining  factors  constant.    Do  the  same  for  the  other  factors.  How  will  you  make  sure  the  other  factors  have  been  held  constant?    Be  sure  to  consider  how  you  will  measure  the  manipulated  variable  and  the  period,  the  responding  variable.    What  could  be  done  to  reduce  errors  in  these  measurements?    Based  on  all  these  things  write  a  procedure  or  several  procedures  you  will  use.    As  you  work  with  the  pendulum  in  the  lab  you  should  wear  the  safety  goggles  provided  and  you  should  make  sure  no  one  is  standing  in  the  path  of  your  pendulum.    Later  days  in  the  lab  you  will  follow  your  procedure.    Find  ways  to  divide  tasks  in  the  laboratory  among  group  members  instead  of  having  everyone  focused  on  one  task  at  the  same  time.                                        

Lab:  Simple  Pendulums    Be  sure  to  write  objectively,  though  that  does  not  imply  passively.  Use  complete  sentences  and  proper  English,  though  you  may  use  lists  for  the  materials  and  the  procedure  instead  of  paragraphs.  Try  to  tie  the  writing  of  different  students  together  using  a  uniform  voice.  Make  sure  there  are  clear  transitions  from  one  section  to  another.  Be  sure  to  address  all  of  the  points  noted  below.    Introduction    

What  is  a  simple  pendulum?    What  is  an  oscillation?    What  is  the  period  of  a  pendulum?    

Objective   What  relationships  are  you  looking  for?    

Hypothesis   What  relationships  do  you  expect  to  see?    

Materials   What  equipment  did  you  use?    

Procedure   What  steps  should  someone  take  to  repeat  your  experiment?  Be  explicit  and  very  clear.  Other  researchers  should  be  able  to  replicate  your  experiment  without  any  other  information.    Note:  Steps  taken  in  your  analysis  are  not  part  of  the  laboratory  procedure.    

Data  Points   Record  all  of  your  data  in  table  format.  Be  sure  to  include  labels  and  units.    Present  your  data  graphically  as  well.    

Analysis   Linearize  graphs  when  necessary  to  determine  the  relationship  between  variables.  If  other  types  of  analysis  are  better  suited  to  a  data  set,  use  those  other  types.    Determine  the  relationships  between  the  period  and  the  other  factors  you  examined.      

Error  analysis   Record  the  precision  of  your  measurements.    Record  the  R2  value(s)  of  your  trendline(s).    What  were  the  sources  of  error?    

Conclusion   On  what  does  a  pendulum’s  period  depend?    What  is  the  relationship  between  the  period  and  these  variables?    How  do  these  relationships  compare  to  your  hypothesis?    If  you  were  to  continue  your  research,  what  might  you  do  to  improve  upon  what  you  have  done  or  to  examine  things  you  may  have  missed?